力学学报

STUDY ON TRAJECTORY CHARACTERISTICS OF STEPPED CYLINDRICAL PROJECTILE ENTERING WATER AT SMALL ANGLE

Qi Xiaobin, Shi Yao, Liu Xiyan, Pan Guang

In the process of the high speed water entry of a conical cylindrical projectile at small angle, the initial cavity develops asymmetrically. With the decrease of the water entry angle, the asymmetric phenomenon of the development of the initial cavity is intensified. As a result, the projectile body is subjected to the step abrupt moment, resulting in a large change in its attitude angle, which seriously affects the stability of the projectile's water-entering trajectory, and even the phenomenon of water-entering ricochet occurs. In order to improve the ballistic stability of high-speed projectile during small angle water entry, a stepped cylindrical projectile design scheme is proposed based on the principle of cavitation effect of cavitator. Based on fluid volume multiphase flow model and dynamic mesh technique, the numerical calculation method of the small angle water entry of the supercavitation projectile is established, and the effectiveness of the numerical method is verified by water entry experiments. By comparing the calculation results of the stepped cylindrical shape model and the conical cylindrical shape model, the influence of the cavity evolution characteristics of different projectile shapes on the hydrodynamic characteristics and ballistic stability is obtained. The results show that the shape of the stepped cylinder can accelerate the development of the primary cavity, and there is a phenomenon of multi-cavity fusion. When the angle of attack is 0°, the cavity size does not change after the cavity is fully developed. Under the condition of small angle of attack (5°), the area of the cavity-wrapped body increases, which improves the lift performance of the projectile. In the process of the water entry with small water entry angle, the development of the cavity form in the cone of the projectile has an important effect on the water entry stability. The stepped cylinder shape can effectively accelerate the development of water entry cavity, form a recovery moment to effectively restrain the continuous increase of the angle of attack, and improve the initial ballistic stability of the high-speed projectile in the small water entry angle.

, Available online , doi: 10.6052/0459-1879-23-212

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DYNAMICS AND ATTITUDE CONTROL OF THE ASSEMBLY PROCESS OF ULTRA-LARGE MULTI-MODULE STRUCTURES

Fu Kangqi, Zhang Lerong, Li Qingjun, Deng Zichen, Wu Zhigang, Jiang Jianping

Autonomous robotic assemble is the most promising approach to construct ultra-large space structures in the future. Ultra-large space structures usually is consisted of multiple modules, which requires the robot to perform repetitive tasks such as capturing, installing, and crawling on the flexible structure. In addition, the structure is affected by space environmental forces during the assembly process and experiences the growth in configuration and changes for parameters, which makes its dynamic behaviors very complicated. In order to study the assembly process of ultra-large multi-module structures in space, a simulation framework is proposed for the orbit-attitude-structure coupled dynamics, planning, and control. Firstly, natural coordinate formulation and absolute nodal coordinate formulation are used to establish an orbit-attitude-structure coupled model for the main structure, space robot, and assembly modules. The Kelvin-Voigt linear spring-damper model is employed to describe the contact and collision for the robot's gripper and the module's docking mechanism. Then, the motion planning, trajectory planning and joint trajectory tracking control of the robot are studied. Finally, dynamic simulations of the assembly process are carried out with different assembly attitude angles and attitude control schemes. Simulation results reveal that the main structure may experience significant orbital drift during assembly (depending on the assembly attitude) due to the change of the center of mass and the orbital difference between the main structure and assembly module. When the structural modules are assembled to the main structure in the radial direction, the semi-major axis and orbital eccentricity of the system will increase greatly. In contrast, the semi-major axis and orbital eccentricity remains unchanged when the structural modules are assembled in the tangential direction. In addition, even if the gravity-gradient-stability attitude is adopted, both attitude control and structural vibration control are necessary to reduce the vibration amplitude of the structures, minimize collision risk between the robot and structure, and improve assembly accuracy and assembly efficiency.

, Available online , doi: 10.6052/0459-1879-23-289

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NONLINEAR DYNAMIC ANALYSIS OF HIGH SPEED AND HEAVY LOAD HERRINGBONE GEAR TRANSMISSION

Mo Shuai, Zeng Yanjun, Wang Zhen, Zhang Wei

Herringbone gears have strong bearing capacity, large contact ratio and high reliability, and are mostly used in high-speed and heavy-load working occasions. Exploring the nonlinear dynamic characteristics of high-speed and heavy-duty herringbone gear transmission system and finding out the stable operation interval of the system can provide reference for its design. Firstly, the time-varying meshing stiffness of gear pair is calculated, and the time-varying meshing force is calculated by introducing the backlash, the nonlinear function of backlash and the comprehensive transmission error. The bearing clearance is introduced to calculate the bearing force. Subsequently, the nonlinear dynamic equation of the high-speed and heavy-duty herringbone gear transmission system is established, and the fourth-order Runge-Kutta method is used to solve the equation. Finally, the influence of different factors on the stability of the system is explored. Keeping other parameters of the system unchanged, the meshing damping, backlash, meshing stiffness and excitation frequency are changed respectively. The time-displacement image, time-velocity image, spatial phase diagram, spatial frequency diagram and bifurcation diagram of the system are drawn. The change trend of nonlinear dynamic response of the system is observed and the motion state of the system is judged. The results show that within a certain range, the stability of the system is positively correlated with meshing damping and meshing stiffness, and negatively correlated with the backlash. When the external excitation frequency is gradually increased, the system motion gradually changes from single-cycle motion to chaotic motion, and then returns to stable single-cycle motion. Therefore, in order to ensure the smooth operation of the system, the external excitation frequency should be reasonably selected.

, Available online , doi: 10.6052/0459-1879-23-166

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RECENT ADVANCES IN ATOMISTIC FRACTURE SIMULATIONS

Ding Bin, Gao Yuan, Chen Yuli, Li Xiaoyan

The fracture of materials/structures is a complex and multi-scale process, which is associated with the rupture of atomic bonds. Hence, the evolution of atomistic crack configurations plays a vital role in the macroscopic fracture behavior. With the swift advancement of experimental technology, the cracks at the atomic scale can be detected by high-resolution electron microscopes, and enhanced computing resources have made atomistic simulation a powerful tool to uncover the underlying fracture mechanisms and to investigate the fracture behaviors of various nanostructured materials. In this review article, we first introduced the common loading approaches for atomistic fracture simulations, including uniform loading, velocity gradient loading, K-field loading and hydrostatic stress loading. After comparing these loading approaches, we further summarized a few methods of calculating fracture toughness based on atomic scale information, including energy release rate method, stress-strain curve integral method, critical stress intensity factor method, cohesive zone method at atomic scale and J-integral method at atomic scale. Then, we reviewed the latest computational studies on several typical types of nanostructured materials (including single-crystalline, polycrystalline and twin structures, amorphous structures and heterogeneous interface structures), like the crack resistance of passivated single-crystalline silicon solar cells, the brittle-to-ductile transition of amorphous silicon anodes controlled by lithium concentration in lithium-ion batteries, and the spontaneous interface delamination driven by mismatch stress. These study results revealed the underlying mechanisms behind the experimental phenomena, and were in good agreement with the experimental results. The consistence between simulation and experiment results confirms the reliability and accuracy of atomistic fracture simulations. Finally, we highlighted some challenges faced by atomistic simulations for fracture of materials and proposed the potential future directions.

, Available online , doi: 10.6052/0459-1879-23-281

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STUDY ON FLOW FIELD PREDICTION OF TURBINE BLADES BY COUPLING SIMILARITY PRINCIPLE

Guo Zhendong, Cheng Hui, Chen Yun, Jiang Shoumin, Song Liming, Li Jun, Feng Zhenping

Computational fluid dynamics (CFD) is an important tool to evaluate the performance of turbine blades and etc. in the design stage. However, the numerical simulation of turbine blades that based on CFD method can be very time-consuming, which makes it rather difficult to meet the need of rapid iteration in the design process of turbine blades. In order to evaluate the performance of turbine blades rapidly and overcome the problem of insufficient generalization ability of pure data-driven prediction models as well, inspired by the concept of physics augmented machine learning, a novel method for turbine blade flow field prediction with strong generalization ability is proposed, by combining the similarity principle with deep learning model. Taking the prediction of the isentropic Mach number distribution at the surface of turbine blades as an example, we propose to make use of the similarity principle to normalize the geometric variables and aerodynamic parameters of turbine blades, and then prepare the training sample set and train the deep learning-based prediction model in the normalized parameter space. And accordingly, a unified prediction model based deep learning can be obtained, which can quickly predict the aerodynamic performance of turbine blades that in very different geometric size and have different boundary condition values. After finishing the model training, the trained prediction model is used to predict the flow fields of the turbine blades that works under different operation condition and of different shape in normalized design space, the flow fields of real-world blades of different size/different working conditions, and the flow fields of different section profiles of GE-E³ low-pressure turbines. The results showed that the predicted results were in good agreement with the CFD evaluation results, and the averaged relative error was less than 1.0%, which verify the accuracy and generalization ability of the proposed flow field prediction model coupling the similarity principle.

, Available online , doi: 10.6052/0459-1879-23-382

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A REVIEW OF NUMERICAL METHODS FOR MODELLING PARTICLE BREAKAGE

Liang Shaomin, Feng Yuntian, Zhao Tingting, Wang Zhihua

Granular materials exist widely in nature and engineering fields. Particles may break under external loads. The breakage behavior of granular materials will cause changes in their physical and mechanical properties, which will have a great effect on engineering and construction. The study of the breakage behavior of particles at macro and micro scales can not only reveal the mechanical mechanism of particle breakage, but also provide guarantee for the safety and normal operation of the engineering field. Therefore, the analysis of particle breakage process has both practical engineering significance and theoretical research value. In this paper, the numerical analysis methods of particle breakage behavior are reviewed. Among the numerical methods based on discrete element method (DEM), the bonded particle model (BPM) and fragment replacement method (FRM) are introduced. In the method based on discrete element-finite element coupling algorithm, the proportional boundary finite element method, combined finite element-discrete element method (FDEM) and cohesive zone model (CZM) are introduced. In addition, the Peridynamics (PD) method is introduced in detail. The proposal, implementation process, development, key issues, advantages and disadvantages of the above numerical methods are summarized and discussed. In addition, the research results at home and abroad and the main applications in engineering are reviewed for each numerical method, and the key issues of each method are introduced. Finally, the current numerical research on particle breakage is summarized, and the future development direction is briefly prospected.

, Available online , doi: 10.6052/0459-1879-23-215

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MULTI-BLOCK LAGRANGIAN ADAPTIVE MESH REFINEMENT NUMERICAL SIMULATION ON THE MULTI-MATERIAL PROBLEM UNDER HIGH-EXPLOSIVE DETONATION DRIVING

Zhou Rui, Li Li, Tian Baolin

The multi-material problems under high-explosive detonation driving exist extensively in the engineering applications. Lagrangian method has been applied widely in the numerical simulation of these problems, because it can simulate the material interface with high fidelity. Refining mesh is one of the common ways to improve the simulated accuracy. However when the resolution is improved through the global mesh refinement, the robust and the efficiency of Lagrangian calculation become worse. It is very necessary to develop an unstructured multi-level Adaptive Mesh Refinement (AMR) method based on the Lagrangian hydrocode for the multi-material and multi-block problems. In present study, a new AMR strategy is proposed, where an unstructured hierarchical data structure is designed. The multi-level meshes are stored in the unstructured hierarchical data structure, and then they are flattened onto the finest global unstructured mesh for the Lagrangian calculation. To adapt the multi-material and multi-block problems, an adaptive coupling algorithm with sliding interface is developed. This implementation preserves the benefits of an unstructured hierarchical data structure. It also avoids the complexity of time adaption and interlevel coupling using boundary conditions in moved Lagrangian mesh, when the solutions are obtained on every level of a refinement hierarchy. At the same time, this new AMR method can be well adapted to multi-block and multi-material problems. The correctness of the unstructured Lagrangian AMR method is verified by the 1D and 2D detonation problems. A series of multi-material problems under high-explosive detonation driving, including multi-material corner detonation, multi-block multi-material problem and detonation propagation in the small curved channel and so on, are simulated using the proposed unstructured AMR. The numerical results show excellent compatibility and performance for the different complex multi-material problems, and it can save more than 90% of the mesh number. The research is an important foundation for further research on the physics mechanism of detonation constraint problem.

, Available online , doi: 10.6052/0459-1879-23-256

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A DYNAMIC VIBRATION ABSORBER ARRAY METHOD FOR MULTI-MODE VIBRATION MITIGATION OF MISTUNED INTEGRALLY BLADED DISK

Wang Shuai, Sun Lei, Wu Jun, Zheng Zhaoli, Fu Hailing, Bi Chuanxing

Integrally bladed disks are the key components of new-generation high-performance aero-engines and have the advantages of compactness, light weight and high thrust-to-weight ratio. Nevertheless, integrally bladed disks also possess the characteristics of low structural damping, high modal density and random mistuning issues, which lead to large vibration amplitudes during passing through the resonant regions. These issues have significantly affected the reliability and fatigue life of integrally bladed disks. In order to effectively mitigate the large vibration amplitudes of mistuned integral blisk, a dynamic vibration absorber array method is developed. The dynamic vibration absorber array consists of a series of vibration absorbers, which are then divided into several series to target multiple different modes and reduce the resonant peaks. In order to reveal the multi-mode vibration mitigation mechanism of the dynamic vibration absorber array approach, a classical lumped parameter model with 3 degrees of freedom per sector is employed for the dynamic modeling of the integral blisk-dynamic vibration absorber array system. The analytic power flow approach is also adopted for quantifying the dissipation and transition of energy between different components and adjacent sectors. On this basis, the influences of the mass, frequency tuning accuracy and damping level of the vibration absorbers, as well as the number of absorbers, on the device’s vibration attenuation performance are comprehensively investigated. A test bench of integral blisk with 12 sectors is set up, and several dynamic vibration absorbers have been designed and manufactured. Experiment has been conducted to validate the effectiveness of the dynamic vibration absorber array approach. The results show that the dynamic vibration absorber array can effectively control the blade-dominant and blade-disk coupling modes. A device with very small mass can usually acquire satisfactory multi-mode vibration attenuation performance for tuned and mistuned integral blisk, and the robustness of performance is also very good.

, Available online , doi: 10.6052/0459-1879-23-336

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THERMAL PULSE-INDUCED EDGE CRACKING OF COATINGS BASED ON TIME-FRACTIONAL HEAT CONDUCTION

Chen Shaohua, Chen Xuejun

Edge cracking due to thermal shock is a common failure mode of coatings that seriously affects their protective performance, so it is crucial to accurately predict the thermally induced growth behavior of edge cracks. In this paper, based on the Caputo time-fractional heat conduction model, the crack driving force for an edge crack in the coating is investigated under a heat flow pulse. Firstly, the closed-form solutions are obtained for transient temperature and thermal stresses by using techniques of Laplace transform and finite cosine integral transform. Secondly, the thermal stress intensity factor (TSIF) for an edge crack is determined by using the princicipal of superpostion and weight function method. The dependence of TSIF is examined on such parameters such as the fractional-order, normalized crack length as well as normalized time. The results show that, the peak value of the TSIF increases as the fractional-order increases. Compared with the case of fractional order super-diffusion due to a heat flow pulse, the classical Fourier thermal diffusion underestimates the crack driving force for an edge crack, while compared with the case of fractional order sub-diffusion, the classical Fourier thermal diffusion overestimates the crack driving force. Under a heat flow pulse, the peak value of TSIF for a shorter edge crack is higher and thus shorter edge cracks are more prone to propagation.

, Available online , doi: 10.6052/0459-1879-23-134

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INSIGHT INTO PRESSURE DROP AND VISCOUS LOSSES IN TIP-LEAKAGE FLOW BETWEEN A HYDROFOIL AND STATIONARY ENDWALL

Xiang Qiujie, Chen Weisheng, Li Yaojun, Liu Zhuqing

Viscous losses and local pressure drop due to tip-clearance flow are the primary factors for efficiency decline and tip-clearance cavitation in axial-flow hydraulic machinery. In this paper, the tip-clearance flow between a NACA0009 hydrofoil and a stationary endwall is investigated using very large eddy simulation, with the aim of exploring the viscous loss properties and the underlying mechanism of pressure drop in the tip-gap region. A quantitative model for the evaluation of viscous losses has been proposed based on the analysis of mean-flow kinetic energy conversion and transport, and the viscous losses and pressure drop associated with the tip-clearance flow are extensively discussed. Gross features of the tip separation vortex (TSV), tip-leakage vortex (TLV), and induced vortex (IV) have been revealed by investigating the mean-flow fields. The production of turbulent kinetic energy (TKE) is found to be the dominant contributor to pressure drop in the TSV, while pressure drop in the TLV is mainly affected by TKE production as well as the convection and transport of mean-flow kinetic energy. In the tip-clearance region, the dissipation of TKE is the main contributor to the viscous losses, accounting for 91.2% of the total losses. The flow structures in the tip gap region have different influences on TKE production. It shows that the shear flow close to the suction surface of the hydrofoil mainly generates the TKE component $\left\langle {{\bar u' } {\bar u' } } \right\rangle$, while the tip-clearance vortices mainly generate the components $\left\langle {{\bar v' }{ \bar v' } } \right\rangle$ and $\left\langle {{\bar w' } {\bar w' } } \right\rangle$. The analysis of the mechanism of TKE production indicates that the TKE production term component P_vw is the dominant contributor to TKE production in both TLV and TSV, suggesting that reducing the spanwise derivative of the pitchwise velocity $ {{\partial \left\langle {\bar v } \right\rangle } \mathord{\left/ {\vphantom {{\partial \left\langle {\bar v } \right\rangle } {\partial z}}} \right. } {\partial z}} $ in the TSV and TLV is a potential way to reduce TKE production, and then alleviate the viscous losses associated with turbulent dissipation in the tip-clearance region. The findings provide a reference for tip-clearance flow control.

, Available online , doi: 10.6052/0459-1879-23-046

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EXPERIMENTAL STUDY ON VISCOUS NEWTONIAN DROPLET IMPACTS ON DRY OR PRE-WETTED MESHES

Zong Shaoqiang, Xu Long, Hao Jiguang

Droplet impacts on meshes are ubiquitous both in nature and in a variety of applications. The impact may lead to liquid penetration through the mesh and formation of secondary droplets underneath the mesh, or spreading on the mesh and no occurrence of penetration. In either situation, liquid remains on the meshes and forms pre-wetted meshes after impacts, leading to different following impact outcomes compared with impacts on dry meshes. However, previous studies focused on impacts of low-viscosity droplets on dry meshes. The evolution and mechanism of viscous Newtonian droplets impacts on dry or pre-wetted meshes remain to be explored. In this paper, the liquid fingers and the fragmentation occurred underneath the mesh following a viscous droplet (aqueous glycerol solution) impacting a dry or pre-wetted mesh are investigated using high-speed shadow imaging technology, with special attention paid on the influence of mesh size, droplet viscosity and pre-wetted liquid film thickness on impact outcomes. It was observed that both a decrease of mesh size and an increase of droplet viscosity resulted in a decrease of maximum length of liquid finger and suppressed a complete penetration through a dry mesh, an increase of pre-wetted liquid film thickness suppressed a complete penetration and resulted in a decrease of maximum length of liquid finger. Considering the influence of mesh size, droplet viscosity, and pre-wetted liquid film thickness, theoretical models for predicting the maximum length of liquid finger when incomplete penetration occurs and for predicting the threshold parameters for complete penetration is proposed and is validated by comparisons with experimental results.

, Available online , doi: 10.6052/0459-1879-23-344

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A MAGNETIC SLIDING AIRFOIL FLUTTER ENERGY HARVESTER

Li Zhiyuan, Lyu Wenbo, Ma Xiaoqing, Zhou Shengxi

Wind-induced vibrations are a common occurrence in nature and have great potential as a viable energy source. Effectively harvesting energy from the structure’s large amplitude response caused by wind-induced vibrations can power microelectronic devices, however, it is still a significant challenge in the field of energy harvesting. In order to efficiently harvest wind-induced vibration energy, this paper proposes a magnetic sliding airfoil flutter energy harvester. A dynamic model of the harvester is established based on a semi-empirical nonlinear aerodynamic model and the electromechanical coupling coefficient related to the position of the magnets. An experimental prototype is created and a wind tunnel test platform is built. In the experiment, by increasing and decreasing the wind speed, two different initial states are provided for the harvester, and two cut-in wind speeds are discovered 5.2 m/s and 8.3 m/s. A sudden jump phenomenon occurs at 8.3 m/s in downward sweeping wind speed experiments. Two jump points and a multi-solution region are found at 6.8 m/s and 8.2 m/s in numerical simulations. The displacement response exhibits a sine waveform, while the output voltage shows a non-sinusoidal waveform with significant even-order harmonics. The simulated plunging displacement and voltage output waveform closely match the experimental waveform, confirming the accuracy of the model. The output root mean square voltage of the energy harvester increases with the increase of resistance, and the average power shows an increasing-then-decreasing trend with resistance. An analysis is conducted on the impact of load resistance on energy harvesting performance. At the wind speed of 8.6 m/s, the average power in the experiment reaches its maximum value of 7.5 mW when the load resistance is close to the coil’s resistance. Overal, this article provides a new design approach for efficient flutter-based energy harvesters, offering a reference for the design of other forms of wind-induced vibration energy harvesters such as galloping-induced and vortex-induced vibration.

, Available online , doi: 10.6052/0459-1879-23-330

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RESEARCH PROGRESS OF PIEZOELECTRIC WIND ENERGY HARVESTERS BASED ON VORTEX-INDUCED VIBRATION

Huang Haobo, Cao Di, Zhou Zhiyong, Du Wenfeng

In recent decades, with the rapid developments of IoT, there appear lots of independent low-energy -consumption electronic devices, e.g., the wireless sensors, portable medical devices, and microelectronic systems, how to provide reliable, clean and self-sufficient power for these devices is posing a great challenge. Providing power to distributed electronic devices through traditional chemical batteries is proving to be difficult. These batteries inherently possess a limited operational lifespan, and the exponential increase in the number of micro-electronic systems has consequently made replacement costs rise dramatically. Moreover, the disposal of the used batteries poses significant risks to the natural environment. In contrast, wind energy is a green energy, it also has advantages such as extensive distribution, substantial storage capacity, and non-pollution. Consequently, harvesting wind energy and converting it into electric energy have attracted wide attention. However, the current scheme of turbine generator is exhibiting some defects, e.g., it requires a great amount of capital, demands a place featuring plenty wind, produces noise in working, covers a large area, and poses a threaten to wildlife. Thus, how to harvest low-speed wind energy efficiently with simple and cheap structures becomes a hot topic of research. Wind energy harvesting based on vortex-induced vibration is emerging as one of the most attractive technologies. It is considered as a potential solution to realize self-powering of the distributed wireless sensors in IoT. In this paper, the research progress of vortex-induced vibration energy harvester is introduced from the aspects of working principle, research progress and promotion schemes. We review and discuss the effects of enhancing schemes, such as optimization of bluff body, introducing nonlinear restoring force, and designs of multidirectional and hybrid harvester, on the energy harvesting performance of vortex-induced vibration wind energy harvester. This review may provide a reference for the design of vortex-induced vibration energy harvesters and improvement of harvesting performance. Finally, according to the current research status, the key challenges are summarized and consulted. The future research direction and prospect are presented and discussed.

, Available online , doi: 10.6052/0459-1879-23-364

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CORRECTION AND DYNAMICAL ANALYSIS OF CLASSICAL MATHEMATICAL MODEL FOR PIECEWISE LINEAR SYSTEM

Zhang Ruiliang, Shen Yongjun, Han Dong

Due to the existence of gap, many mechanical systems can be simplified into piecewise linear models, where the auxiliary spring system (ASS) usually contains damping. In most classical mathematical models established in the literatures, the contact point and separation point of the primary system and ASS are generally fixed at the gap. In this paper, it is found that due to the different mechanical characteristics of the spring and damper in the ASS, the positions of the contact point and separation point actually change with the system parameters and motion state. If this case is ignored, the subsequent dynamical analysis including bifurcation and chaos may incur errors. In this paper, based on the classical mathematical model of piecewise linear system, it is firstly demonstrated through numerical solution that the primary system is prematurely separated from the ASS before returning to the gap under harmonic excitation, which explains the incorrectness of the classical model. Based on the classical mechanical model, the further study shows that there is not only the premature separation but also contact hysteresis in the primary system. Accordingly, a more reasonable mathematical model is proposed by correcting the contact and separation conditions. It is found that the contact point, separation point and the amplitude-frequency response of the corrected model differ greatly from the classical mathematical model, and the characteristic of complex dynamics may change after correction, which proves that the corrected model is more reasonable and can better reflect the engineering reality. Then, the integration interval of the averaging method is generalized so the analytical solution of amplitude-frequency response after correction is obtained. The correctness of analytical solution is verified through the Runge-Kutta method and the stability discrimination formula is obtained through the analytical solution. Finally, the influence of the parameters of the ASS on the amplitude-frequency response is explored.

, Available online , doi: 10.6052/0459-1879-23-295

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VIBRATION REDUCTION MECHANISM OF NONLINEAR ZENER SYSTEM UNDER COMBINED PARAMETRIC AND EXTERNAL EXCITATIONS

Xing Jingdian, Li Xianghong, Shen Yongjun

The aim is to reveal the vibration reduction mechanism of nonlinear Zener systems with different scales under the combined parametric and external excitation. With the Duffing system as the main system, low-frequency parametric excitation and external excitation are introduced, and the system is changed into a 1.5-degree-of-freedom nonlinear Zener system by coupling the viscoelastic element. After comparing the time history diagram and phase diagram before and after the change of the system, it is found that the system changes from a single large-amplitude vibration of the excited state to the bursting vibration of the excited state and the silent state, the vibration amplitude is greatly reduced, and the vibration reduction effect is obvious. Then analyze the stability and bifurcation of autonomous systems. The stability of the generalized autonomous system, the close relationship between the imperfect bifurcation and the vibration behavior of the non-autonomous system are analyzed based on the idea that there is a maximum value of the external excitation in the range of the excitation amplitude change by using the method of envelope fast and slow analysis, which defines the parameter excitation term as a slow-varying parameter. It is found that the autonomous system has an obvious regulating effect on the non-autonomous system, which is manifested in the enhanced stability of the equilibrium point of the autonomous system after coupling viscoelastic elements, the type of equilibrium point changes from center to stable focus, the enhanced attraction of the equilibrium line to the system track line, and at the same time, multiple stabilized equilibrium lines limit the vibration region of the non-autonomous system, which are the fundamental reasons for vibration reduction. In addition, based on the analysis of dual parameter bifurcation, it was found that adjusting parameters can control the occurrence of the system imperfect bifurcation, thereby improving the system's vibration reduction performance.

, Available online , doi: 10.6052/0459-1879-23-294

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STUDY ON THE INFLUENCE OF TEMPERATURE ON THE SIZE OF PARTICLES DEPOSITED IN IMPACTOR

Peng Hui, Chi Hui, Xu Cong, Yin Zhaoqin, Bao Fubing, Tu Chengxu

The properties of microparticles are almost closely related to the particle size. In order to study the characteristics of aerosol particles, it is necessary to obtain particle size distribution information. The inertial impactor is a device based on the principle of inertia to realize the deposition separation of particles of different sizes in the atmosphere. During actual use, it experiences complex and changeable environments. In this paper, the Lagrangian multiphase (LMP) model is used to numerically simulate the gas-solid two-phase flow in the impactor. The effect of aerosol temperature variation (−40°C ~ 60°C) on the particle deposition rate was investigated using the finite volume method (FVM) under both adiabatic and heat transfer conditions, and its effect on particle size separation was analyzed. The results show that: under the condition of wall adiabatic, as the temperature of the aerosol increases, the particle deposition position diverges from the center of the impact plate to the edge, the particle collection efficiency decreases, and the number of particle collection decreases gradually; in the condition of aerosol and wall heat transfer, as the temperature of the aerosol increases, the deposition position of large particles diverges from the center of the impact plate to the edge, and the collection efficiency of particles decreases, while the opposite is true for small particles. In addition, there is an intersection point in the particle collection efficiency curves at different aerosol temperatures, and the collection efficiency of large and small particles on both sides of the intersection point changes oppositely with temperature. By studying the influence of temperature on the impactor particle collection, the results of particle diameter separation can be modified and more accurate particle size distribution can be obtained.

, Available online , doi: 10.6052/0459-1879-23-316

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FLOW-INDUCED VIBRATION ENERGY HARVESTING BASED ON FINNED METASURFACE BLUFF BODY

Zhang Ye, Wang Junlei

The metasurface has a significant effect on the aerodynamic characteristics of bluff bodies. To promote the flow-induced vibration energy harvesting (FIVEH) performance of ordinary cylinder, several heights and numbers of finned metasurfaces are assembled on the ordinary cylinder and their effects on the FIVEH characteristics are investigated. The FIVEH experimental platform is set up and the piezoelectric energy harvesters are fabricated, the energy harvesting performance of different energy harvesters is analyzed experimentally. Based on the coupling model of vortex-induced vibration and galloping proposed by Tamura and Shimada (Tamura-Shimada model), the fluid-structure-electric coupling theoretical model for single-degree-of-freedom (SDOF) piezoelectric energy harvester is derived and the influence of aerodynamic parameters on the energy harvesting performance is elaborated. The computational fluid dynamics (CFD) model is conducted to simulate the vortex shedding patterns and flow field characteristics of different bluff bodies. The experimental results show that the finned metasurface has a remarkable impact on the dynamic characteristics of the bluff body: suppressing vortex-induced vibration (VIV) contributes to the high-level performance degradation of the energy harvesting, or transforming VIV to galloping, thus significantly improving the energy harvesting performance. When the wind speed exceeds the corresponding galloping cut-in speed, the piezoelectric energy harvester shows the galloping characteristics and occurs the stable limit cycle oscillation (LCO). The theoretical model can accurately predict the voltage characteristics. The CFD simulation results show that the finned metasurface can influence the wake vortex strength of bluff bodies then lead to a different dynamic response, thus affecting the energy harvesting performance. In addition, the influence of different interface circuits on the output power of piezoelectric energy harvesters is investigated, compared with the standard direct current (DC) circuit, the self-powered synchronous charge extraction (SP-SCE) circuit not only enhances the output power of the piezoelectric energy harvester but also provides more stable power output, the requirement of impedance matching is resolved and the flexibility of adjusting the high-performance piezoelectric energy harvester for practical applications is guaranteed.

, Available online , doi: 10.6052/0459-1879-23-298

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EXPERIMENTAL STUDY ON DRAG REDUCTION BY AIR INJECTION ON HYDROPHILIC AND ALTERNATED SUPERHYDROPHOBIC SURFACES

Guo Peiyang, Zhang Yi, Zhang Mengzhuo, Hu Haibao

The s uperhydrophobic surface is conducive to the formation of gas film on the wall, which is a potential new bionic drag reduction technology with potential anti-fouling function. However, the gas film is easy to be lost and damaged under the shear action of high-speed incoming flow. By constructing the hydrophilic and alternated superhydrophobic surfaces to enhance the stability of the superhydrophobic surface gas film, thus expect to achieve a better drag reduction effect. Using a gravity type water circulation pipeline testing system, The influence of superhydrophobic strip width and Reynolds number on drag reduction performance under turbulent conditions were tested. In addition, the corresponding gas film spreading state and its impact on drag reduction characteristics were analyzed. The results show that the continuous air injection of the hydrophilic and alternated superhydrophobic surfaces can solve the problem of the loss of the air film layer on the surface and realize the stable maintenance of the air film layer for a long time; the surface drag reduction rate shows a decreasing tendency with the increase of the water flow rate (Reynolds number), and the stability of the surface air film layer decreases gradually; the surface drag reduction rate shows a tendency of increasing and then decreasing with the increase of the width of the superhydrophobic strips and reaches a maximal reduction rate of 40.2% at the width of the superhydrophobic strips of 5.0 mm. The reason for this is that when the superhydrophobic strip is narrower, the liquid-solid interface with high shear stress accounts for a higher percentage, which brings a higher resistance; and when the strip is wider, the stability of the air film layer on the surface is not good. Therefore, the most suitable width of superhydrophobic strip exists under a certain flow condition, which makes the best drag reduction effect.

, Available online , doi: 10.6052/0459-1879-23-303

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NONLINEAR DYNAMICS CHARACTERISTICS OF TUMBLER-INSPIRED ELECTROMAGNETIC ENERGY HARVESTERS

Pan Xiagui, Yu Ning, Yan Bo

Ocean wave energy, as a prominent renewable source, possesses the potential to be harnessed for the generation of electricity, specifically catering to the power requirements of wireless sensors. It will be the key promoting the digital evolution of the marine environmental monitoring systems. However, the low-frequency and large randomness characteristics restrict the efficient harvesting of ocean waves. The tumbler structure has ultra-low frequency vibration characteristics that are different from traditional structures, and it is sensitive to low-frequency excitation, which can absorb surrounding vibration energy. In this paper, we design a tumbler-inspired electromagnetic energy harvester with a Halbach array, aiming to enhance the performance of low-frequency wave energy harvesting by constructing magnetic nonlinear forces. The theoretical model of the harvester is established according to the Lagrange’s equation. The analytical responses of the tumbler's swing angle and the harvester's voltage are derived by the harmonic balance method. The analytical solution is compared with the numerical solution. Moreover, simulations are conducted to investigate the effect of different excitation conditions such as excitation amplitude and frequency on the dynamic response characteristics of the system. Finally, a prototype of the tumbler-inspired electromagnetic energy harvester was fabricated, and an experimental platform was built. It verifies the correctness of the theoretical model. Both the simulation and experimental results show that the harvester exhibits the hardening stiffness characteristic through introducing magnetic nonlinearity. This characteristic is beneficial to enhance the low-frequency energy harvesting efficiency. The harvester exhibits diverse dynamic behaviors such as periodic motion, quasi-periodic motion, and chaotic motion with the change of the excitation amplitude and frequency. In addition, low frequency and large excitation are more likely to cause chaotic motion, which is beneficial to energy harvesting effect. This study provides a theoretical support for the design and application of the tumbler mechanism in low-frequency ocean wave energy harvesting.

, Available online , doi: 10.6052/0459-1879-23-332

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A COMPARATIVE STUDY ON THE TORSIONAL VIBRATION ATTENUATION OF CLOSED-LOOP INTERNAL COMBUSTION ENGINE SHAFTING USING TUNED MASS DAMPER AND NONLINEAR ENERGY SINK

Ma Kai, Du Jingtao, Liu Yang, Chen Ximing

Traditional linear vibration absorber has long been used in vibration suppression, but its performance is limited by its narrow bandwidth. Considering that the cyclic excitation force of closed-loop shafting of internal combustion engine varies with the speed, it is necessary to achieve efficient vibration reduction in a relatively wide frequency domain. In order to investigate the feasibility of nonlinear energy sink (NES) replacing tuned mass damper (TMD) to suppress the torsional vibration of crankshaft, a multi-inertias nonlinear closed-loop self-excited coupled oscillation model (M-NCSCO) is established in this study. Based on this, the effects of TMD and NES on torsional vibration of crankshaft are studied. The transient and steady-state torsional oscillations at different coaxial segments of shafting are considered comprehensively in the analysis process. In addition, three functions of vibration density, performance lead efficiency and fluctuation ratio are defined to consider the performance of the dynamic vibration absorbers (DVA). The efficiency and robustness of NES and TMD under different design parameters (variable stiffness, variable damping and variable position arrangement) are discussed. The results show that NES and TMD have different stiffness and damping failure interval when controlling crankshaft torsional vibration. With the change of design parameters, NES and TMD lead the performance of vibration reduction alternately, with a combined performance of 24.5% for NES and 3.3% for TMD. At the same time, NES has a high damping dependence (13.6%), TMD has a high stiffness dependence (3.6%) and position dependence (25.6%).

, Available online , doi: 10.6052/0459-1879-23-285

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FLOW-INDUCED VIBRATION CHARACTERISTICS ANALYSIS OF EPR FUEL RODS BASED ON POD METHOD

Min Guangyun, Feng Linna, Jiang Naibin

The length of the EPR (European Pressurized Reactor) fuel rod is longer compared to the M310 fuel rod, resulting in a decrease in frequency and an increase in amplitude compared to the M310 fuel rod. Under the influences of the coolant, Grid-To-Rod Fretting (GTRF) wear may be exacerbated, potentially leading to the leakage of radioactive materials. Here, the EPR fuel rod is simplified as a 3D beam model, where the constraints of dimples and springs on the fuel rod are treated as equivalent elastic constraints. Additionally, the fuel rod with a spacer grid is further simplified as a multi-span continuous simply supported beam model. A finite element model of the EPR fuel rod based on ANSYS-APDL is established, and the fundamental principles of wet mode analysis and vibration response analysis are explained. 12 grid failure conditions have been sorted out, and the influences of grid failure on wet mode and vibration response have been systematically studied. A method for analyzing the vibration characteristics of the EPR fuel rod using the Proper Orthogonal Decomposition (POD) method is proposed, targeting Flow-Induced Vibration (FIV) of the EPR fuel rod. The snapshot matrix is decomposed by POD method to generate the projection subspace, and the responses are projected onto the subspace for model reduction. Finally, the response is reconstructed in the physical space. The results show that the amplitude of vibration responses would increase at the location of grid failure; When the grid structure fails and causes the EPR fuel rod model to become a cantilever beam configuration, the maximum response to turbulent excitation is achieved; For the analysis of response, the first 2 orders POD Reduced Order Model (ROM) can basically reconstruct the response of the fuel rod. The research in this paper will help to the optimization and design of nuclear reactor engineering.

, Available online , doi: 10.6052/0459-1879-23-243

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ANALYSIS OF THE EFFECT OF THE THERMAL AXIAL FORCE ON THE THERMOELASTIC DAMPING IN BI-LAYERED MICRO BEAMS

Li Shirong

In recent years, there have been many publications on the TED of composite laminated beam/plate resonators. However, the contribution of the thermal axial force (or thermal membrane force) on the thermoelastic damping (TED) in the resonators were neglected in all those investigations. It is well known that if the distribution of material properties along the thickness is asymmetric about the geometric midplane of a beam/plate resonator then the physical neutral surface will deviate from it. As a result, the temperature field in the resonator arising in the thermoelastic coupling vibration will produce both the thermal bending moment and the thermal axial/membrane force each of them will produce the TED. In this paper, based on the Euler-Bernoulli beam theory and the classical heat conduction theory, mathematical formulations for the thermo-elastically coupled free vibration of bi-layered laminated micro beams with rectangular cross sections are established in which the contribution of the thermal axial force on the internal energy dissipation is considered accurately. Then, analytical solutions of the thermal axial force and bending moment are found in terms of the geometric quantities representing the beam deformation. Furthermore, the complex frequency of the system and the TED representing by the inverse quality factor are obtained. As an example of numerical analysis, a bi-layered micro beam with homogenous layers of silver (Ag) and silicon nitride (Si₃N₄) is selected to quantitatively examine the effects of the thermal axial force on the TED by changing the volume fractions of the laminas and the total thickness of the beam. The numerical results show that neglection of the thermal axial force will underestimate the TED in the bi-layered beam resonators. Especially, for the resonator with the volume fraction of the silver at 70% (that of the silicon nitride at 30%), the TED will be underestimated about 16.3% if the thermal axial force is neglected.

, Available online , doi: 10.6052/0459-1879-23-381

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PIEZOELECTRIC VIBRATION ENERGY HARVESTERS AND DYNAMIC ANALYSIS BASED ON THE SPINNING BEAM

Zhao Xiang, Yuan Mingze, Fang Shitong, Li Yinghui

In order to study the piezoelectric vibration energy harvesting problem of the forced vibration of a spinning beam structure under the combined effect of axial forces and external excitation on the beam, this paper proposes to use the Green's function method to solve the analytical solution of the voltage under the forced vibration of the spinning piezoelectric energy harvester. The extended Hamilton's principle and PZT-5A piezoelectric constitutive relationship are used to develop a force-electric coupling model for the spinning piezoelectric energy harvester of forced vibration based on the Euler-Bernoulli beam theory. Utilizing the Laplace transform, the explicit expressions of the Green's function of the coupled vibration equations can be acquired. Based on the linear superposition principle and the physical significance of the Green's function, the coupled system equations are decoupled to find the analytical solution of the voltage of the spinning piezoelectric energy harvester under forced vibration. In the numerical calculation, the validity of the solution of this paper is verified by comparing the present solution with the result of the existing literature as well as experimental result. The relationship between the piezoelectric response and physical parameters such as resistance and spinning speed of the energy harvester is analyzed separately. This research suggests that piezoelectric response of the spinning energy harvester increases with increasing resistance until the resistance reaches the optimal load resistance; the maximum output voltage of the energy harvester can be increased by turning up the spinning speed; by reducing the axial force, the high fundamental frequency of the energy harvester can be improved while maintaining the efficient operation of the energy harvester.

, Available online , doi: 10.6052/0459-1879-23-328

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MULTI-OUTPUT PHYSICS-INFORMED NEURAL NETWORKS MODEL BASED ON THE RUNGE-KUTTA METHOD

Wei Chang, Fan Yuchen, Zhou Yongqing, Liu Xin, Zhang Chaoqun, Wang Heyang

Physics-informed neural networks (PINN) have attracted considerable attention in the field of intelligent scientific computing primarily due to their capacity to incorporate prior knowledge of physics. This outstanding integration allows PINNs to automatically satisfy physical constraints even with limited or zero labeled data. As a result, the applicability and effectiveness of PINN are vastly developed across numerous domains. However, it is worth noting that the discrete time models of PINN, also known as PINN-RK, face a significant limitation in their ability to approximate multiple physical quantities and solve coupled partial differential equation systems simultaneously. This shortcoming hinders its ability to handle complex multi-physics fields, which is a crucial drawback in various practical scenarios. To overcome this limitation, a multi-output physics-informed neural network based on Runge-Kutta method (MO-PINN-RK) is proposed in this paper.MO-PINN-RK, building upon the success of PINN-RK, incorporates a sophisticated parallel neural network architecture, boasting multiple output layers for enhanced performance and accuracy. By associating each output layer with a sub-network and assigning it with different physical quantities, MO-PINN-RK can accurately solve the coupled partial differential equation system and predict multiple physical quantities simultaneously. The MO-PINN-RK proposed in this paper overcomes the limitation of PINN-RK that is only applicable to one dimensional problems extending its applicability to more general multi-dimensional problems. To demonstrate the effectiveness of MO-PINN-RK, it is then applied to the flow field prediction and parameter identification of flow around a cylinder. The outcomes unequivocally reveal that MO-PINN-RK surpasses PINN in terms of flow field prediction precision, achieving an enhancement of no less than 2 times. At the same time, MO-PINN-RK reduces the relative error by an order of magnitude in the context of parameter identification. This highlights the exceptional capabilities of MO-PINN-RK in the field of fluid dynamics, offering a more accurate and efficient solution for solving complex problems.

, Available online , doi: 10.6052/0459-1879-23-299

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THE SYMPLECTIC METHOD FOR THE BUCKLING/POST-BUCKLING PROBLEMS OF RECTANGULAR PLATES ON A TENSIONLESS ELASTIC FOUNDATION

Xiong Sijun, Zheng Xinran, Liang Li, Zhou Chao, Zhao Yan, Li Rui

The buckling/post-buckling problems of rectangular thin plates on a tensionless elastic foundation constitute an important class of topics in mechanics of plates and shells, with extensive applications in engineering. Due to involving contact nonlinearity, this kind of problems have been primarily solved using numerical methods, while the development of analytical methods with significant benchmark value is currently a challenge. To address the aforementioned issue, a plate is divided into several subproblems in this paper, each containing enforced boundary conditions. The subproblems are solved analytically using the separation of variables and the symplectic eigen expansion in the symplectic space. The contact state between the plate and the foundation is determined by the continuity conditions at the boundaries of the subproblems. By iteratively solving the above process, the convergent division of the subproblems is obtained, along with the buckling load and buckling mode shape of the plate. The results indicate that there are significant differences in the buckling behavior between a plate on a tensionless elastic foundation and that on a Winkler foundation. The stiffness of the tensionless elastic foundation has a significant influence on both the buckling loads and buckling mode shapes. Based on this, the post-buckling problem of a rectangular plate on a tensionless elastic foundation is solved by combining the Koiter perturbation method with the symplectic method, yielding the post-buckling equilibrium path of the plate. The obtained buckling and post-buckling results both agree well with those by the finite element method, which confirms the correctness of the present results. Due to the rigorous mathematical derivation and high computational efficiency of the method proposed in this paper, it not only provides a valuable theoretical tool for the study of buckling/post-buckling behaviors of rectangular thin plates on a tensionless elastic foundation, but also can be extended to solve more complex mechanical problems of plates and shells.

, Available online , doi: 10.6052/0459-1879-23-384

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FLUID–SOLID COUPLING STUDY OF AIRWAY TISSUE DEFORMATIONS UNDER AIRFLOW

Qin Yuan, Chen Xi, Wei Dong, Ren Xiaoyong, Xu Guangkui

The uvulopalatopharyngoplasty (UPPP) is a common surgical procedure used to treat obstructive sleep apnea (OSA). However, due to the unclear mechanism of action, it is not possible to achieve the ideal success rate for the surgery. The current studies mostly overlook the specific morphology of the patient’s upper airway or the elastic deformation of the airway soft tissues, which results in the existing results not being sufficient to effectively guide surgical treatment. In this study, we constructed an accurate three-dimensional upper airway model based on CT scan images of OSA patients before and after surgery, and simulated and studied the elastic deformations of soft tissues in the upper airway through bi-directional fluid-structure interaction (FSI) calculation. We compared the flow velocity, pressure distribution, and elastic deformation of the upper airways in successful and failed cases of surgery for OSA, and explained the cause of OSA and the mechanism of surgery from the perspective of fluid flow in the airway and deformation of the airway soft tissues. Our results showed that the size of the minimum cross-sectional area is not the decisive factor for the success of UPPP surgery. Successful surgery can reduce the negative pressure level on the airway walls and decrease the pressure drop between the inlet and outlet of the airway. In addition, by using the bi-directional FSI method, we further simplified a two-dimensional soft palate model to investigate the influence of the soft palate’s elastic modulus on the inhalation process. It is found that a softer palate can improve the flow field’s flow state when the elastic modulus of the soft palate is within the range of 0.5 MPa to 1.5 MPa, yet it is also more prone to deform and collapse. The fluid-solid coupling model developed in this study provides a research tool for personalized prediction of surgical outcomes.

, Available online , doi: 10.6052/0459-1879-23-278

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METHOD OF POLYNOMIAL VECTORS FOR NONLINEAR VIBRATION SYSTEMS

Jin Dongping

The perturbation methods for nonlinear vibration systems make it necessary to solve a set of second-order ordinary differential equations (ODEs), which are obtained by equating the like power of the perturbation solutions respectively. One of the main drawbacks of the ODEs-based methods is of low efficiency, especially for nonlinear vibration systems of multiple degrees of freedom. In this paper, a method of polynomial vectors for solving the approximate solution of nonlinear vibration systems is proposed. The second order ordinary differential equations are written in a set of state equations of the first order first, wherein the nonlinear terms of the state equations are expressed as the products of a constant matrix and a polynomial vector with the like power. By using the direct perturbation method, the linear non-homogeneous equations are obtained for the like power approximations, while the nonlinear terms are written as the products of the constant matrix and the polynomial vector with the previous approximate solutions as its element. Furthermore, the multiplication of polynomials in the polynomial vector is expressed in matrix form via Toeplitz matrix, and then all approximate analytical formulas of the state equations are determined by the first-order non-homogeneous equations. Results show that the proposed method based upon the state equations yields a concise calculation for nonlinear vibration systems of multiply degrees of freedom.

, Available online , doi: 10.6052/0459-1879-23-331

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RESEARCH ON THE LATTICE BOLTZMANN ALGORITHM FOR GRID REFINEMENT BASED ON NON-UNIFORM RECTANGULAR GRID

An Bo, Meng Xinyu, Yang Shuangjun, Sang Weimin

The traditional lattice Boltzmann method (LBM), especially the classic single-relaxation model (SLBM) based on the uniform square grid, has poor robustness and numerical stability, which limits the development and applications of LBM. Grid refinement strategy can effectively alleviate this dilemma, however for the traditional LBM, the grid refinement will inevitably lead to a sudden drop in computational efficiency and a rise in equipment requirements. Therefore, in order to solve this problem, based on the non-uniform rectangular grid, combined with the idea of interpolation LBM, the 25-bit Lagrangian interpolation LBM is proposed on the premise of ensuring the local grid refinement for the surfaces and area with severe flow changes, and the computational accuracy as well. Taking the classic lid-driven cavity flow for instance, a comparative analysis including different grid resolutions and interpolation schemes is performed. The verification includes both the numerical simulations of steady states and unsteady periodic solutions. The results show that the Lagrangian interpolation scheme performs better than other interpolation schemes. In this paper, the local grid refinement is able to ensure the capture of the flow details adjacent to surfaces and in the area of intense flow changes. The numerical algorithm can provide reliable results for numerical simulations. Meanwhile, the total grid number is greatly reduced, as a result the computational efficiency is greatly improved; The numerical simulation method has good robustness and is suitable for numerical simulations for both steady states and unsteady solutions.

, Available online , doi: 10.6052/0459-1879-23-062

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RESERCH ON UNIVERSAL SOLUTION OF TRANSFORMING SEPARABLE CONVEX PROGRAMMING TO DUAL PROGRAMMING WITH EXPLICIT MODEL

Peng Xirong, Sui Yunkang

This paper aims to improve the modeling and solving level of DP-EM (dual programming-explicit model) method. Based on the characteristics of a class of convex programming with separable variables, the DP-EM model breaks through the usual way of using second-order approximation for the dual objective function, and derives an explicit dual objective function. The DP-EM method is more efficient than the dual sequential quadratic programming (DSQP) and the method of moving asymptotes (MMA) when it is applied to the ICM method solving the continuum topology optimization problems. In this paper, the common explicit models are abstracted into universal separable convex programming, and then converted into DP-EM models under certain conditions. Four processing methods are proposed: (1) The approximate solution of iterative approximation of dual variables; (2) The solution of objective and constraint functions with the exponential function form; (3) The solution of objective and constraint functions with the power function form; (4) Accurate solution based on variable transformation. In order to conduct numerical verification, extensive calculations have been carried out. Limited by paper space, five representative examples among them are listed. Example 1 is a pure mathematical problem, which is used to compare the efficiency of the processing method 1 and the processing method 4. The remaining four examples are all continuum topology optimization problems modeled and solved by the ICM ( independent continuous and mapping) method, including displacement, stress, fatigue constraint problems and fail-safe optimization. Those four examples are illustrations of the processing method 3. All the results show the universality of the proposed method and the higher solving efficiency. The proposed method can used for different penalty functions in the variable density method and filtering functions in the ICM method. And the proposed method is more efficient than the MMA method. The contribution of the work is as follows: (1) In depth, it deepens the research on the dual solution of structural optimization; (2) In breadth, it makes a contribution to the dual theory of mathematical programming.

, Available online , doi: 10.6052/0459-1879-23-267

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RESEARCH ON QUASI-ZERO-STIFFNESS-ENABLED PIEZOELECTRIC LOW-FREQUENCY VIBRATION ENERGY HARVESTING METHOD

Chen Tingting, Wang Kai, Cheng Li, Zhou Jiaxi

The bottleneck in the rapid development and widespread deployment of the Internet of Things (IoT) is how to power tens of thousands of sensor network nodes in an efficient and cost-effective way. The conversion of vibration energy into electrical energy for self-powering of the sensor is a very feasible solution. However, low-frequency components make up a large proportion of environmental vibrations, and traditional vibration energy harvesting methods have difficulty in efficiently converting low-frequency ( < 10Hz) vibration energy, which limits the widespread use of vibration energy harvesting technology in the field of IoT. In this paper, a quasi-zero-stiffness-enabled piezoelectric vibration energy harvester (QZSE-EH) is proposed for the harvesting of the ultra-low frequency energy from the environment, human body and some mechanical devices. At first, the electromechanical coupling equation of the energy conversion unit is obtained by using the energy method, and the dynamic and electrical response equations are solved by using the harmonic balance method. The effect of the damping ratio and the excitation amplitude is explored by means of the results of the analytical solution. Finally, a prototype of the QZSE-EH was fabricated and the experiment was carried out to verify the correctness of the dynamic and electrical output response of the system. The results show that when the frequency is 2.5Hz, the maximum peak voltage of a single energy conversion unit in the QZSE-EH reaches 25V. The QZSE-EH proposed in this paper is expected to overcome the problem that the operating bandwidth of conventional resonant piezoelectric energy harvesters depends on the natural frequency, and the multi-stable energy harvesters are unable to cross the barrier, making ultra-low frequency and low-amplitude energy harvesting extremely difficult. This paper provides a new idea for the efficient harvesting of ultra-low frequency and low-amplitude vibration energy, and can further consolidate the theory of vibration energy harvesting.

, Available online , doi: 10.6052/0459-1879-23-315

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OPTIMAL DESIGN OF RUDDER STRUCTURES BASED ON DATA-DRIVEN METHOD

Shi Guanghui, Jia Yibo, Hao Wenyu, Wu Wenhua, Li Qiang, Lin Ye, Du Zongliang

In the field of aerospace engineering, there is a growing demand for lightweight design based on structural topology optimization; specifically, the rudder structures of many high-tech equipment serve in severe thermal and mechanical environments, and it is both challenging and important to carry out efficient lightweight design of them. For a given load, the stiffness of thin-walled structures can be significantly enhanced by introducing stiffening ribs or reinforcing stiffeners, and this design philosophy is well consistent with the design requirement of air rudders. However, traditional stiffening ribs design under an implicit topology optimization framework suffers from a huge number of design variables, low computational efficiency, difficulty in guaranteeing the geometric characteristics of stiffening ribs, and inconvenience in directly importing optimization results into CAD systems. In this study, a new explicit topology optimization method (i.e., Moving Morphable Component (MMC) method) is adopted, and combined with the data-driven methodology for efficient design of stiffening ribs in air rudders with irregular closed geometry. This method directly optimizes the geometric information of the stiffening ribs, and has the advantages of fewer design variables, high computational efficiency, and seamless connection between the optimization results and CAD software, so as to solve the issues of long optimization cycle and strong dependence on the experience of designers faced with the implicit topology optimization method and subsequent redundant steps such as model reconstruction and parameter optimization. Furthermore, the mapping between rib layout and key mechanical properties is described through an artificial neural network model, and used as a surrogate model for optimization to efficiently obtain high-quality initial designs, thus significantly improving the efficiency of the design optimization of rudder structures. The design framework presented integrates the structural topology optimization with artificial neural network model, which can be applied to the intelligent design of other key equipment.

, Available online , doi: 10.6052/0459-1879-23-187

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RESEARCH ON THE AERO-HEATING AT THE SHARPENED LEADING EDGE BASED ON NONLINEAR COUPLED CONSTITUTIVE RELATIONS

Yang Junyuan, Li Xudong, Zeng Shuhua, Zhao Wenwen, Zhang Fu, Chen Weifang

The aerodynamic heating effect of a representative sharpened leading-edge model under hypersonic continuous/rarefied flow conditions is investigated through the integration of numerical simulation and wind tunnel testing methodologies in this study. Based on a three-dimensional finite volume framework, the sharpened leading-edge model is numerically analyzed using the nonlinear coupled constitutive relations (NCCR) model, facilitating the accurate representation of local rarefied non-equilibrium flow and surface heat flux. The performance of the NCCR model in describing the sharpened leading-edge is evaluated and corroborated in comparison with the experimental data. Under wind tunnel test conditions at an equivalent altitude of 33 km, it is observed that the discrepancy between the peak heat flux coefficient at the stagnation point computed by the NCCR model and the experimental data is a mere 1.31%, . Moreover, the peak heat flux coefficient at the stagnation point obtained by the Fay-Riddell formula and the Navier-Stokes (NS) equations is within 5% according to the experimental value, the coefficient of heat flux at other locations on the surface is also well maintained from the experiment value, i.e., the deviations is within a range of 10%, which proves that the local rarefied gas effect near the sharpened leading-edge of the aircraft has a weak effect on aerodynamic heating. In contrast, at an equivalent altitude as high as 60 km, the effect of local rarefied gas near the sharpened leading-edge on aerodynamic heating is obvious, and the deviation between the coefficient of heat flux at the stagnation point with the help of the NS equations and the experimental data amounts to 33.31%. The deviation of the peak heat flux coefficient at the stagnation point calculated by the Fay-Riddell formula is 29.5% in terms of the experimental value. However, the variation in stagnation heat flux coefficient obtained from the NCCR model remains comparatively low at 11.77%. It shows the advantages of the NCCR model for solving rarefied nonequilibrium flows.

, Available online , doi: 10.6052/0459-1879-23-171

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INVESTIGATION ON MODULATION OF ACOUSTIC WAVES THROUGH WATER-AIR INTERFACE BY COMBINED METASURFACES

Zhang Shaocong, Zhu Jiahui, Li Chenyang, Weng Jiaxuan, Wang Yanfeng, Wang Yuesheng

Acoustic metasurfaces are a kind of artificial structure with carefully designed microstructures and spatial order. They can exhibit exotic wave behaviors beyond the nature. So they are attracting more and more attentions by researchers from different disciplinary fields. However, most existing studies on metasurfaces focus on single medium such as air or water. Sound manipulation through trans media is rarely investigated. In this paper, we focus the modulation of sound waves through water-air interface by using the combined metasurfaces. Firstly, genetic algorithm is used to design airbone metasurface with high transmission and wavefront control capability. Then, the combined metasurfaces are designed by integrating a discrete metasurface with unitary amplitude through water-air interface to achieve the wavefront manipulation of acoustic waves with high transmission. The impact of the coupling spacing between combined metasurfaces on wave manipulation is also discussed. Finally, samples of the combined metasurfaces are fabricated, and experimental measurement of the acoustic focusing is conducted. The results indicate that abnormal transmission and focusing of acoustic waves through water-air interface can be realized by combining the two independently designed metasurfaces. Coupling spacing of the combined metasurfaces significantly affects the sound modulation through water-air interafce. When the coupling spacing is small, although the combined metasurface can realize the manipulation of the acoustic waves through water-air interface, the manipulation performance is relatively poor. With the increase of the coupling spacing, the manipulation performance of the combined metasurface on the trans interface improves rapidly and then becomes stable. The acoustic focusing of sound across water-air interface is observed by employing the combined metsaurfaces in the experiment. And the influence of the coupling spacing on acoustic focusing is also obtained. Experimental results are generally in good agreements with the simulations. This research provides numerical and experimental foundations for the design of novel acoustic devices through water-air interface.

, Available online , doi: 10.6052/0459-1879-23-293

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STUDY ON THE EFFECT OF TRANSVERSE JET ON THE ASYMMETRIC AERODYNAMIC CHARACTERISTICS OF SLENDER SPINNING BODIES WITH LOW SPEED AND LARGE ANGLE OF ATTACK

Xu Yihang, Liu Wei

In this paper, a combination of wind tunnel tests and numerical simulations is used to analyse the large angle of attack asymmetric characteristics of a slender spinning body with and without lateral jets at Reynolds number Re = 55000. The wind tunnel tests reveal the difference between the large angle of attack asymmetric aerodynamic characteristics of the slender spiniform in the normal and lateral directions of the jet and those in the absence of the jet, and the asymmetric aerodynamic characteristics of the slender spiniform with and without the lateral jet under several typical operating conditions are analysed by means of numerical simulations. The wind tunnel tests reveal that the cyclone with no jet, jet in the windward region and jet in the leeward region exhibit different asymmetric flow characteristics when the elongated cyclone is controlled normal to the windward region. The direction of the lateral force coefficient changes after the angle of attack is greater than 40º, and is the same as the direction of the lateral force coefficient when there is no jet, but its absolute value is smaller than the lateral force coefficient when there is no jet. Secondly, when the jet is located in the leeward zone, the angle of attack between 15º and 35º with the jet is significantly larger in absolute value than without the jet, and the lateral force coefficient changes between 40º and 70º in the subsequent cyclone in a similar pattern to that without the jet. When the slender spinning body for lateral control due to the direct force generated by the jet along the lateral direction, so that the angle of attack range between 0º ~ 20º and more than 45º with the jet of the spinning body lateral force coefficient absolute value is greater than without the jet, but the angle of attack between 25º ~ 40º when the spinning body lateral force coefficient absolute value decreases, and even at 35º almost zero. Numerical simulations have shown that when the long, slender spiniform is controlled normal to the windward and leeward areas of the jet, the jet has an effect on the flow separation on the side with the spoilers, making the flow field structure different from that without the jet. In the absence of jets, the flow separation occurs first on the side of the slender spiniform with the spoiler, but in the presence of jets the flow separation occurs first on the side without the spoiler, resulting in an increase in the absolute value of the lateral force and a change in the direction of the lateral force. When the slender spiniform is laterally controlled, the flow is separated first on the side without spoilers and later on the side with spoilers. The spin body with spoiler side due to the influence of the jet in the vicinity of the nozzle and the rear of the cartridge produced a low-pressure area, no spoiler side of the flow separation after the spin body in the rear part of the high-pressure area, so that the cartridge produced a positive lateral force along the z-axis, which is the opposite direction of the direct force generated by the jet, the size of the same, so that the spin body angle of attack between 20º ~ 40º less lateral force, or even at 35º the situation is almost zero.

, Available online , doi: 10.6052/0459-1879-23-251

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A FLOW FIELD SUPER-RESOLUTION RECONSTRUCTION METHOD BASED ON DIFFUSION MODEL

Han Yang, Zhu Junpeng, Guo Chunyu, Fan Yiwei, Wang Yonghao

Low-resolution flow field data contains limited information, which fails to fully capture the detailed evolutionary processes of the flow field. Especially for the random turbulent features and small-scale vortex details in turbulence, they are even more challenging to obtain, thereby restricting the in-depth investigation of flow field evolution mechanisms. In order to address this limitation and reconstruct high-resolution data from low-resolution flow fields, this paper proposes a generative diffusion model called FlowDiffusionNet for flow field super-resolution reconstruction. The model takes the low-resolution flow field data input as the constraint condition, and utilizes a denoising fraction matching method to reproduce high-resolution flow field data. FlowDiffusionNet's structural design takes into consideration both the low-frequency information and high-frequency spatial features of flow field data, employing a diffusion-based modeling technique to reconstruct the residuals for high-resolution data. The proposed model's architecture is amenable to transfer learning, allowing its application to degraded flow fields at different levels. The performance of FlowDiffusionNet is evaluated on various classical flow field datasets and compared against other methods such as Bicubic interpolation, Super-Resolution Generative Adversarial Network (SRGAN), and Super-Resolution Convolutional Neural Network (SRCNN). The results demonstrate that the proposed method achieves the best reconstruction performance on various flow fields, especially for flow field data with small-scale vortex structures down sampled by a factor of 4, where the objective evaluation index Structural Similarity Index Measure (SSIM) reaches 0.999.

, Available online , doi: 10.6052/0459-1879-23-167

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NONLINEAR ELECTROMECHANICAL MODELING OF PENDULUM-TYPE TRIBOELECTRIC NANOGENERATORS

Han Qinkai, Gao Shuai, Shao Qingyang, Chu Fulei

By reasonably designing the pendulum length, the natural frequency of a pendulum structure can be effectively reduced, so that it can realize resonance under low frequency (even ultra-low frequency) vibration excitation, and then greatly improve the energy conversion performance. The pendulum-type triboelectric nanogenerator (P-TENG) has naturally become the focus of academic attention. In this study, nonlinear electromechanical coupling modeling and parameter sensitivity analysis are conducted to optimize the structural design of the P-TENG, so as to promote its development towards engineering practicability. Based on the analysis of power generation mechanism, an equivalent capacitance model is proposed. Combined with the energy principle and equivalent circuit method, an electromechanical coupling model considering the nonlinear variation of pendulum angle is established. Using the harmonic balance method and alternated frequency/time domain technique, the steady-state output of the P-TENG is solved analytically, and the stability of the results is determined. Numerical integration and dynamic tests are conducted to verify the accuracy of analytical model. The results are compared with the linear model and the influence of various design parameters on the output characteristics of the P-TENG is investigated. Considering the nonlinear effects, the estimated operating bandwidth of the model increases significantly (by a relative increment of 83%). The proposed model can effectively avoid the underestimation of the operation bandwidth and significantly improve the accuracy of the P-TENG performance estimation. Increasing the excitation amplitude, reducing the damping ratio, and minimizing the electrode angle can improve the output performance of the P-TENG. Various fitting models have been proposed to model the relationship between design parameters and output performance. The fitting coefficients obtained from the parameter influence discussion can be used as the basis for the P-TENG output performance design.

, Available online , doi: 10.6052/0459-1879-23-197

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ALUMINUM PLATE DEFECT DETECTION BASED ON MULTILEVEL LSTM

Zhang Fengyi, Wang Lihua, Ye Wenjing

Aluminum plates are widely used in fields such as aviation, aerospace, and construction due to their excellent fatigue resistance and ductility. However, during the production process, various defects can occur due to external environmental factors, operating processes and so on. These defects can affect the mechanical properties of aluminum plates, such as reducing their strength, ductility, and toughness, which leads to a shortened service life. This article proposes a method of using a multilevel long short-term memory (LSTM) neural network for assisting the detection of inclusions (void defects) in aluminum plates under the condition of single transmission and reception of ultrasonic waves. The propagation of ultrasonic waves in an aluminum plate containing inclusion defects is simulated using the finite element software COMSOL Multiphysics. Waveform data containing defect information is then derived. By training the waveform data, a neural network model reflecting the relationship between waveform data and the size and location of inclusions is obtained. In addition, we adopt a hard voting method to alleviate the problem of complex parameter adjustment during network training and improve the reliability of the detection results. The results show that the accuracy of radius detection for inclusion defects exceeds 98%, the accuracy of depth detection for inclusion defects reaches 1, and the accuracy of horizontal position detection for inclusion defects exceeds 95%. It provides reference for the application of LSTM neural network in ultrasonic non-destructive testing.

, Available online , doi: 10.6052/0459-1879-23-193

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DYNAMIC MODELING AND VIBRATION AND NOISE REDUCTION OF AUTONOMOUS UNDERWATER VEHICLES BASED ON RESONANCE CHANGER

Zhang Kangyu, Lu Kuan, Cheng Hui, Fu Chao, Guo Dong

In this paper, the vibration-acoustic model of the autonomous underwater vehicle (AUV) with nonlinear bearings is proposed based on the research background of vibration noise suppression and its concealment improvement. By finding the optimal design parameters of resonance changer (RC), the vibration and sound power level generated by the shell is minimized to achieve the purpose of anti-resonance. Firstly, the FEM of double-beam system with propeller-shaft-shell by Lagrange method is established. The nonlinear factors of bearing based on Hertz contact theory are added, and then the acoustic dipole radiation field model is derived according to the principle of sound propagation. Secondly, the Runge-Kutta method is used. The dynamic characteristics are analyzed by post-processing signals such as time domain response, spectrum, bifurcation diagram and amplitude-frequency response. Finally, the shell sound power level as the cost function is used and the parameters of the RC are designed. By comparing the two supports of nonlinear bearing and linear spring, it is found that the main trend of the sound power level of AUV shell under the former is distributed along the linear spring, which is lower, and reaches the peak in the corresponding resonance region. In addition, the results show that the RC can greatly reduce the resonance response amplitude and sound power level, noteworthily, the effect is the most significant at the resonance frequency design point. The frequency at the resonance frequency design point does not be shifted, however, the resonance frequency has a certain offset in other individual intervals in addition to reduction of the maximum resonance amplitude value. The theoretical model of this paper reveals the dynamic response characteristics of AUV and the influence law of parameters. The research results can provide new improvement ideas for the optimization design of vibration and noise reduction of AUV, and have certain theoretical guiding significance.

, Available online , doi: 10.6052/0459-1879-23-217

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INVESTIGATION ON THE IMPACT OF UNDERWATER VEHICLE HEAD SHAPES ON THE FLOW AND PRESSURE CHARACTERISTICS OF VENTILATED CAVITY UNDER VERTICAL EMISSION CONDITIONS

Ren Zeyu, Wang Xiaogang, Quan Xiaobo, Cheng Shaohua

This paper aims to explore the impact of underwater vehicle head shapes on the evolution of ventilated cavity under vertical emission conditions. Firstly, based on the finite volume method, the numerical calculation model for ventilated cavitation under the vertical emission condition is established, in which the Improved Delayed Detached Eddy Simulation, the volume of fluid multiphase flow model and the overlapping mesh technique are adopted. Subsequently, compared with the vertical emission experiments, the validity of the numerical method was confirmed for predicting ventilated cloudy cavity, which demonstrates the applicability of the method in the complex unsteady calculation. Finally, the study compares the flow and pressure characteristics of ventilated cavity of streamline head and blunt head vehicle under the same working conditions, and the reasons for the observed differences are analyzed from the perspective of vortex dynamics. The results indicates that, compared to streamlined-head vehicle, the ventilated cavity of the blunt-headed vehicle experiences a smaller velocity gradient at the gas-liquid interface and is more influenced by gravity and buoyancy, leading to an earlier nonlinear instability under the action of the Rayleigh-Taylor instability mechanism. Additionally, the cavity shows more dramatic unsteady flow characteristics, e.g. floating behavior and cavity shedding, which influence the flow separation at the end of the ventilated cavity of the blunt-headed vehicle, resulting in suppression of high amplitude characteristics of stagnation high pressure.

, Available online , doi: 10.6052/0459-1879-23-230

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RESEARCH ON TORSIONAL VIBRATION SUPPRESSION OF CHIRAL METAMATERIAL INERTER DYNAMIC VIBRATION ABSORBER

Li Hui, Wei Guochong, Yao Hongliang, Peng Xi

The inerter structure has proven to be highly effective in vibration suppression, exhibiting remarkable vibration reduction capabilities. The new type of dynamic vibration absorber combined with inerter and vibration absorber has the advantage of light weight. However, the complex design of traditional inerter structures hinders their widespread adoption in vibration control applications. In view of this limitation, a chiral metamaterial inerter dynamic vibration absorber (CIDVA) with simple and efficient inerter structure is designed in this paper. The CIDVA combines the advantages of both inerter and vibration absorber technologies, notably its lightweight design. Firstly, the compress-torsion coupling effect of chiral metamaterials is introduced, and the effect is used to amplify the torsion stroke of the inerter disk to form the inerter mechanism. In order to ensure the feasibility of the inerter mechanism, an auxiliary mechanism is designed to ensure the movement of chiral metamaterials. Secondly, the structure and working principle of CIDVA are thoroughly examined, and the finite element simulation analysis is carried out to accurately calculate and verify its inertance amplification constant. Building upon this foundation, the dynamic equation of the CIDVA-primary system is established, enabling a comprehensive study of the torsional vibration suppression abilities of the CIDVA-main system under steady-state and transient excitations. A comparison with the locked CIDVA configuration is also performed. Furthermore, the validity of the achieved inerter is meticulously analyzed. Finally, to validate the torsional vibration suppression capabilities of CIDVA on the main system, experimental verification is conducted. The simulation and experimental results demonstrate that CIDVA can effectively suppress the torsional vibration of the primary system under both transient and steady-state excitation, surpassing the performance of traditional DVA. Notably, CIDVA achieves significant weight savings, reducing its own moment of inertia by more than 10 times compared to traditional DVAs. and can save more than 10 times of its own moment of inertia compared with the traditional DVA. It provides new ideas and methods for DVA to achieve lightweight design and efficient vibration suppression. These findings contribute novel ideas and methodologies for achieving lightweight design and efficient vibration suppression in the field of DVAs.

, Available online , doi: 10.6052/0459-1879-23-189

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A THEORETICAL STUDY ON NEAR-BLOWOFF CHARACTERISTICS OF RECIRCULATION-ZONE STABILIZED COMBUSTION

Wang Hongbo, Lian Chengyue, Zhang Jincheng, Zeng Yu, Yang Yixin, Wang Yanan

A theoretical framework has been developed for recirculation-zone stabilized combustion near lean blowoff, based on the assumption that the flame is stabilized in the adjacent shear layer. Once the flame is stabilized in the shear layer, the fluid approaching the flame is actually a mixture of the free stream and the recirculating flow since the shear layer simultaneously entrains fluids from both sides. If the flame is lean, the recirculating flow would essentially consist of products and excess oxygen but no fuel, the mixture approaching the flame should thus be leaner than the free stream. Accordingly, even if the free stream is flammable, the equivalence ratio of the mixture in the shear layer may be outside of the flammability limits. Analyses show that, for a recirculation-zone stabilized lean flame, the effective equivalence ratio of the mixture approaching the flame stabilized in the shear layer is lower than that of the free stream due to the existence of the recirculation zone. A diagram of regimes for the recirculation-zone stabilized combustion near lean blowoff is then constructed according to the theoretical analyses, which involves four parameters: the freestream equivalence ratio, the shear-layer entrainment ratio, the blowoff limit and the reignition limit. In the diagram, four regimes have been identified: a super-stable flame, a sub-stable flame, an oscillating flame and blowoff. In particular, the identification of an oscillation region in the parameter space is impressive, which introduces an intrinsical instability mechanism that has not previously been noted for near-blowoff flames. In this mechanism, the equivalence ratio oscillations in the shear layer are indeed driven by the combustion process since the position/oscillation of the flame affects the fluid composition entering into the recirculation zone and thus the equivalence ratio in the shear layer. Therefore, the feedback loop between the equivalence ratio oscillations and the combustion process is closed accompanied with periodic blowoff and flashback/re-stabilization of the flame.

, Available online , doi: 10.6052/0459-1879-23-206

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DYNAMIC STABILITY AND INFLUENCE FACTORS OF THE WHOLE TRAJECTORY OF FIXED CANARD DUAL-SPIN PROJECTILES

Zhao Xinxin, Shi Jinguang, Wang Zhongyuan, Zhang Ning

To research the dynamic stability of fixed canard dual-spin projectiles in full trajectory flight, the state space model of the complex attack angle motion is established under the condition of small attack angle, and the general condition that the real parts of the characteristic roots are all negative is derived by using the Hurwitz method. Based on the motion characteristics of the front body’s rolling angle before/after starting control, the dynamic stability criterion of fixed canard dual-spin projectiles under different flight conditions is proposed by using the stability analysis method of the conventional rotating projectiles, whose form is similar to that of the conventional rotating projectiles. When flying without control, the control force and moment terms of control canard are added correspondingly in the lift force and static moment terms. Controlled flight further increases the relative increment effect of relevant terms. Accordingly, the constraint on canard parameters of control surface is deduced under the condition that the parameters of projectile body are determined, the effects of the control force coefficient’s derivative, the installation position and the deflection angle of control canard on the dynamic stability are discussed, and the reasons for the formation of the dynamic instability of this kind of projectile are revealed. The simulation analysis results of the complex attack angle motion under different conditions show that when the relative increment caused by control surface is within the boundary of both uncontrolled and controlled flight, the full trajectory flight of the fixed canard dual-spin projectile is dynamically stable, which verifies that the dynamic stability criterion and the constraint on canard parameters deduced in this paper are reasonable and feasible, and provides a theoretical basis and design reference for the design and development of this type of projectile.

, Available online , doi: 10.6052/0459-1879-21-636

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