力学学报

2023, 55(1): 1-2.

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REVIEW ON MECHANICAL BEHAVIOR AND CONSTITUTIVE RELATION OF POLYUREA ELASTOMER

Gong Chencheng, Chen Yan, Dai Lanhong

Polyurea is a new type of elastomeric polymer which is formed through the reaction of isocyanate components with amine components. Due to its excellent mechanical property, such as high elongation, high strain rate strengthening and high dissipation, polyurea shows a broad application prospect in the fields of national defense, energy resources and transportation. So far, numerous studies on the static and dynamic mechanical properties of polyurea under multiple temperatures and strain rates have been performed. Various constitutive models were established to characterize and predict its mechanical behavior concerning its temperature dependence, strain rate dependence and other mechanical characteristics. These researches provide a foundation for understanding the anti-impact and shock attenuation mechanism of polyurea, as well as its further application. Firstly, the micro-phase segregated structure of polyurea is introduced briefly in this paper. Then we review the experimental researches on the mechanical behavior of polyurea from the perspectives of linear viscoelasticity under the small deformation and nonlinear viscoelasticity under the large deformation, including the development of testing technology and the researches on the factors influencing the viscoelasticity of polyurea. In addition, the constitutive models of polyurea, established through the framework of multiplicative decomposition of deformation gradient, the approach of hereditary integral, the strain-time decoupling approach or other modelling approaches, are reviewed. The differences between different types of models are discussed from the perspectives of strain rate range, temperature range, whether the model could describe the pressure dependence and softening behavior of polyurea, and the number of model parameters. Finally, several suggestions for further research on the mechanical behavior and the constitutive relation of polyurea are put forward.

2023, 55(1): 1-23. doi: 10.6052/0459-1879-22-455

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PAST AND FUTURE EVOLUTIONS OF FLUID MECHANICS: THINKING TRIGGERED BY THE BATCHELOR CENTENNIAL EVENT

Zhu Wei, Wang Guohua

G.K. Batchelor is one of the giants of fluid mechanics in the in the twentieth century. He had made pioneering contributions in the field of homogeneous turbulence theory and low Reynolds number micro-fluid mechanics. He is the founder of Journal of Fluid Mechanics, one of the top journal in the field of fluid mechanics, and the department of applied mathematics and theoretical physics (DAMTP), whose spirit of pursuing physical and quantitative understanding of fluid flows has impressed the development of fluid mechanics in recent 100 years. He has cultivated and influenced a large number of scholars who have made outstanding achievements in numerous subjects of fluid mechanics, including turbulence theory, experimental fluid mechanics, turbulence stability, environmental fluid mechanics, multiphase fluid mechanics, magneto-hydrodynamics, micro- and nano-scale fluid mechanics, etc. Taking the G.K. Batchelor centennial event as an opportunity, this paper briefly reviews the evolution history of fluid mechanics in the past 300 years, including the three important stages of fluid mechanics: classical stage based on solid mathematics and physics foundation, the modern stage driven by application demands, and the contemporary stage characterized by discipline intersection and integration. Special concerns are concentrated on the formation, merging and inheritance of the distinct styles of the four schools in the modern stage of fluid mechanics in the past hundred years from the perspective of outstanding scholars and their key contributions to the discipline. The driving force and trend of the development of contemporary fluid mechanics are discussed taking wind-blown sand environmental mechanics as an example. It shows that fluid mechanics provides the basis for the development of branch disciplines, while the demands of branch disciplines drives the endogenous development of fluid mechanics which forms a spiral growth relationship. Finally, the progress spectrum and innovation trends of fluid mechanics in the future are revealed and discussed.

2023, 55(1): 24-37. doi: 10.6052/0459-1879-22-531

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PREDICTION OF CROSSFLOW TRANSITION BASED ON DEEP NEURAL NETWORKS

Hu Zhenyu, Wang Zilu, Chen Jianqiang, Yuan Xianxu, Xiang Xinghao

This study based on deep neural networks (DNN), produces a mapping from the physical quantities such as dimensionless velocity gradient and streamwise vorticity of laminar flow field to the intermittency of cross flow transition, and obtains a new data driven transition model. The data driven transition model is coupled with the SST k-ω turbulence model, and the process of solving the transport equations is effectively simplified, which realize efficient and accurate numerical simulation of subsonic 3-D cross flow transition. The computational data of NLF(2)-0415 swept airfoil at different Reynolds numbers is used to train DNN, and two cases are used to test. The prediction accuracy of data driven transition model is similar to that of γ-Re_θ transition model. Using the data driven transition model to compute other typical examples of cross flow transition, to verify its generalization ability. For the transition locations of NLF(2)-0415 swept airfoil with different swept angles, the simulation results of data driven transition model have similar accuracy to that of γ-Re_θ transition model. Moreover, the phenomenon of transition position moving forward and then backward in the process of sweep Angle increasing from 45° to 65° can be predicted by data driven transition model. For the standard ellipsoid, although using low resolution mesh, the data driven transition model has the ability to compute the transition location, and the computed results of C_f are same to those of other transition models and experiments. The results show that coupling data driven transition model (which is obtained from the physical quantities related to cross flow transition) with SST k-ω transition model can realize the general prediction of cross flow transition. On the premise of ensuring computational accuracy, the data driven transition model requires lower resolution mesh and has higher computing efficiency.

2023, 55(1): 38-51. doi: 10.6052/0459-1879-22-448

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EXPERIMENTAL INVESTIGATION ON ACTIVE CONTROL TURBULENT BOUNDARY LAYER DRAY REDUCTION BY SYNCHRONOUS AND ASYNCHRONOUS VIBRATION OF DUAL VIBRATORS

Bai Jianxia, Zhao Kaifang, Cheng Xiaoqi, Jiang Nan

In order to achieve the drag reduction effect, the experimental scheme of zero-mass jet active control turbulent boundary layer is designed independently in the paper. Dual piezoelectric (PZT) oscillators as the active control actuators are symmetrically distributed embedded along the spanwise direction of the flat plate in turbulent boundary layer. The experimental investigation is carried out by synchronous (syn) and asynchronous (asyn) vibration active control mode to achieve drag reduction with the periodic vibration of dual PZT oscillators in a wind tunnel. It realizes the periodic interference and modulation to the multi-scale coherent structure in turbulent boundary layer. Furthermore, it reduces the skin friction and realizes drag reduction effect in all controlled cases.The consequence shows that the maximum drag reduction rate of 18.54% is obtained at 100 V, 160 Hz asynchronous vibration case.The multi-scale wavelet analysis of streamwise velocity shows that the energy of the small-scale coherent structure increases while the large-scale coherent structure decreases in all controlled conditions.Meanwhile, it adjusts the energy distribution of the large-scale and small-scale coherent structures in near-wall regions of turbulent boundary layer .The drag reduction effect of the asynchronous controlled case is better than the synchronous controlled case at the same voltage and frequency of vibration. When the vibration frequency of the PZT oscillators is 160 Hz, the PDF curves of the wavelet coefficient show the fluctuation characteristics and the tails of the PDF curve widen significantly. The pulsations of near-wall regions become more ordered and regular and the turbulence weakens intermittently after control in turbulent boundary layer.The results of the conditional phase averaging of small-scale coherent structure show that the periodic perturbations of the PZT oscillators enhance the turbulence intensity of the small-scale coherent structures. Furthermore, drag reduction effect is also achieved by breaking the large-scale coherent structure into the small-scale coherent structure. As the streamwise position is far away from the PZT oscillators, the modulation effect of the coherent structure in turbulent boundary layer gradually weakens.

2023, 55(1): 52-61. doi: 10.6052/0459-1879-22-248

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INVESTIGATION ON THE HYDRODYNAMIC PERFORMANCE OF A VERTICAL DOUBLE MANTA RAY GLIDING WITH VARIABLE ATTACK ANGLES

Gao Pengcheng, Liu Guanshan, Huang Qiaogao, Pan Guang, Ma Yunlong

In order to investigate the effects of vertical spacing and angle of attack on the hydrodynamic performance of double manta rays when gliding in clusters along the vertical distribution, a computational model of manta rays was developed based on the actual shape of manta rays. Four spacing arrangements, including 0.25, 0.5, 0.75 and 1 times the body thickness, and nine angle of attack states, namely −8°−8°, were set up. Then, the numerical simulation of the double manta ray with variable attack angle and vertical distance was carried out by Fluent software. The mean lift/drag of the system and the lift/drag of each individual in the cluster were analyzed by combining the flow field pressure and velocity clouds. Numerical calculations showed that the average drag of the two manta rays was higher than that of a single manta ray when they glided in groups with attack angles ranging from −8° to 8° in the vertical direction. When the two manta rays glide at negative attack angle, the drag of the lower manta ray decreases, and the smaller the vertical spacing, the more obvious the drag reduction effect is; when the two manta rays glide at positive attack angle, the upper manta ray gains drag reduction. When the two manta ray glide at negative attack angle, the system average lift is greater than that of the single glider; when the two manta rays glide at negative attack angle, the system average lift is less than that of the single glider, and the system average lift is almost independent of the vertical spacing. The lift of the lower manta ray is always greater than that of the upper manta ray, but the difference in lift decreases as the vertical spacing increases.

2023, 55(1): 62-69. doi: 10.6052/0459-1879-22-353

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AERODYNAMIC OPTIMIZATION DESIGN OF THE VORTEX-SHOCK INTEGRATED WAVERIDER IN WIDE SPEED RANGE

Liu Chaoyu, Qu Feng, Li Jieqi, Bai Junqiang, Liu Chuanzhen, Bai Peng, Qian Zhansen

The vortex-shock integrated wide-speed-range waverider could significantly improve aerodynamic performances of the traditional waverider at the low-speed state by introducing vortex effect, and has potential to be widely used in the overall aerodynamic design of the wide-speed-range aerospace vehicle in the future. However, the design of the vortex-shock integrated waverider does not consider the three-dimensional effect, low-speed effect, viscous effect and head/leading edge passivation effect during the establishment of reference flow field. So it still has potential to improve the wide-speed-range performances of the vortex-shock integrated waverider with the aerodynamic shape optimization method. In order to solve this problem, this paper develops an aerodynamic optimization design method for aircraft in wide speed range based on discrete adjoint by combining high-fidelity RANS solver, free deformation parameterization method, robust structural mesh deformation method, discrete adjoint method and sequential quadratic programming algorithm. Through the method, the aerodynamic optimization design in the wide speed range based on discrete adjoint is used to carry out for the vortex-shock integrated waverider in the subsonic and hypersonic flight conditions. The optimum configuration in the wide speed range is obtained through the aerodynamic optimization design and the flow mechanism is analyzed. The results show that compared with the original configuration, the optimum one increases the lift and lift-to-drag ratio of the vortex-shock integrated waverider more than 10% at low speed, while keeping the hypersonic lift and drag aerodynamic performance of the vehicle not fall. The performance improvement of the vehicle at low speed is attributed to the significant enhancement of the leeward vortex effect, resulting in a larger area of low pressure on the leeward surface to effectively increase the lift. The research shows that the gradient optimization based on discrete adjoint could further improve the aerodynamic performances of the vortex-shock integrated wide-speed-range waverider at high and low speed.

2023, 55(1): 70-83. doi: 10.6052/0459-1879-22-412

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A NUMERICAL ALGORITHM BASED ON FICTITIOUS DOMAIN METHOD FOR THE SIMULATION OF MICROORGANISMS SWIMMING IN A VISCOELASTIC FLUID

Peng Fangyuan, Pan Dingyi, Chen Xingfan, Lin Zhaowu

Microorganisms are one of the important parts of natural ecosystem, understanding the kinematic behaviors of microorganisms swimming in complex fluids could provide guidance for the design and manufacturing of MEMS. Wall effects are one of the most important scientific problems of the research of microorganism swimming, and recent work reveals that microorganisms show complicated swimming behaviors near the wall. However, most of the work reported in the literatures focused on microorganism swimming in Newtonian fluid, less attention is paid on microorganism swimming in viscoelastic fluid or other non-Newtonian fluids. A direct-forcing fictitious domain method combined with Cholesky decomposition for the simulation of microorganisms swimming in a viscoelastic fluid is reported in this paper. The squirmer model is applied to represent the swimming of microorganisms. The numerical schemes for the discretization of Giesekus constitutive equation are first presented and validated. The newly developed simulation model is then applied to investigate the effect of planar wall on swimming dynamics of current squirmer in viscoelastic flow, i.e., Giesekus fluid. The results show that the swimming direction of squirmer is a critical factor of the wall-trapping effect. The fluid elasticity affects the swimmer motion near solid wall by generating an elastic torque which reorient the swimming direction. The time for the squirmer to contact planar wall in viscoelastic fluid is almost twice of that in Newtonian fluid.

2023, 55(1): 84-94. doi: 10.6052/0459-1879-22-372

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FULL SOLUTION FOR CHARACTERIZING STRESS FIELDS NEAR THE TIP OF MODE-I CRACK UNDER PLANE AND POWER-LAW PLASTIC CONDITIONS

Wang Zhiqiang, Cai Lixun, Huang Maobo

In the fields of aerospace, ships, oil pipelines and nuclear power, there will be cracks inevitably in structure or component part when running for a long time under extreme conditions. Therefore, it is necessary to explore the features of the stress-strain fields near the crack tip, to study the quasi-static fracture behavior of cracked structures. In this paper, the stress distributions near the tip of mode-I cracked specimens under plane strain and plane stress conditions are studied for power-law hardening material. Based on the energy density equivalence and dimensional analysis, the analytical equation of equivalent stress of representative volume element (RVE) with the median energy density of a finite-dimensions specimen is proposed, and it is defined as the stress factor. Furthermore, for compact tension (CT) and single edge bend (SEB) finite size specimens under plane strain and plane stress conditions, the stress factor is used as a characteristic variable, and a special trigonometric function is assumed to characterize butterfly-wings type or scallop type contour lines of the equivalent stress near the mode-I crack tip, and then a semi-analytical model for compact tension specimens and single edge bend specimens under plane strain and plane stress and fully plastic conditions is proposed to describe the stress fields near the crack tip. As shown in comparing results given by finite element analysis to those predicted by the model for stress fields near the crack tip of the two cracked specimens, all agree well with each other. The semi-analytical model of stress field near the crack tip proposed in this paper is simple in form and accurate in result. It can be directly used to predict the stress distribution near the tip of mode-I crack, which is convenient for fracture safety evaluation and theoretical development.

2023, 55(1): 95-112. doi: 10.6052/0459-1879-22-360

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PHASE TRANSITION AND SPALL BEHAVIOR OF TIN UNDER RAMP WAVE COMPRESSION

Chong Tao, Mo Jianjun, Fu Hua, Li Tao, Luo Binqiang

Obtaining the dynamic response experimental data of tin under different thermodynamic paths is the basis for in-depth study of its phase transition and damage physical process. The ramp wave compression experiment of tin was carried out by using magnetic driving loading device CQ-4, and the dynamic response data of tin were obtained. The experimental results show that in the loading section, tin undergoes elastic-plastic transformation and β-γ phase transition. The yield strength is about 0.2 GPa, and the phase transition onset pressure decreases from 7.54 GPa to 7.14 GPa with the increase of tin thickness. There is obvious spallation damage in the unloading section. The spallation strength is about 1.1 GPa, which is greatly different from the impact test results under the same loading pressure. The thickness of the spallation is about 0.38 mm. Combined with the multiphase equation of state based on Helmholtz free energy, nonequilibrium phase strain rate model and damage evolution equation, the experimental dynamic process is numerically simulated. The calculation results can well describe the three physical processes of elastic-plastic transformation, phase transition and spallation.

2023, 55(1): 113-119. doi: 10.6052/0459-1879-22-516

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SECONDARY ORIENTATION EFFECTS OF NI-BASED ALLOYS WITH COOLING HOLES: A STRAIN GRADIENT CRYSTAL PLASTICITY FEM STUDY

Xiong Yukai, Zhao Jianfeng, Rao Wei, Huang Zhiyong, Kang Guozheng, Zhang Xu

Single crystal Ni-based alloys possess excellent properties such as high temperature resistance, high strength and high toughness. Thses mechanical properties are affected by secondary orientation and cooling holes induced during complex manufacturing processes. The current research mainly focuses on the deformation mechanism and mechanical response of plates with one hole. While, the plate with multiple holes is often used in engineering. At present, it is urgent to clarify the deformation mechanism of the plate with multiple holes, the secondary orientation effect, and the strain gradient effect caused by cooling holes. In this paper, a nonlocal crystal plasticity constitutive model based on the dislocation mechanism is used to numerically simulate the uniaxial tensile deformation behavior of the Ni-based single crystal plate with cooling holes. A dislocation flux term is derived based on the relationship between the plastic slip gradient and geometrically necessary dislocations, enabling this crystal plasticity model to effectively describe the strain gradient effect. In order to comprehensively reveal the secondary orientation effect of Ni-based alloys with cooling holes, this paper systematically studies the uniaxial tensile deformation behavior of sheets with [100] and [110] orientations (two secondary orientations). The influence of the number of holes on the plastic behavior of the plate with two secondary orientations is investigated. By analyzing the variation of the resolved stress on slip systems, activation of the dominant slip systems and the evolution of geometrically necessary dislocation density during the deformation of Ni-based alloy plates, the effects of plastic slip and its distribution on the strength of Ni-based alloy plates with different secondary orientations are discussed. The results show that the tensile strength of [110] plate is lower than that of [100] plate. Furthermore, the plastic deformation process of the five-hole plate is more complicated than that of the one-hole plate and is easier to be affected by secondary orientation. Finally, the location of the slip gradient is mainly located near the cooling hole and the plastic slip zone. The research results can provide theory basis for the design and service of Ni-based alloys in engineering.

2023, 55(1): 120-133. doi: 10.6052/0459-1879-22-497

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STUDY OF WAVE DISPERSION AND PROPAGATION IN PERIDYNAMICS

Zhu Jinggao, Ren Xiaodan

Periydnamics (PD) is a new nonlocal method reformulated from solid mechanics. It adopts the integral form of governing equation and is naturally suitable to model fragments and cracks under extreme events, thus widely applied in the field of national defense security. However, the nonlocality in PD introduces the dispersion effect and imposes adverse effect on wave propagation, which will greatly restrict its capability in capturing solid behaviors, especially the fractures. For this purpose, we employ the spectral analysis method to study the dispersion behavior of PD system comprehensively. It is found that compared to the low frequencies, the dispersion relation of high frequency components shows an oscillation trend and zero-energy modes, leading to more serious dispersion problems. The dispersion behavior of high frequencies changes with the wave propagation direction and shows 45° symmetry in the spatial wave propagation. As the PD system itself is non-dissipative, the adverse effect of the dispersion problem can not be suppressed. As a result, the simulation accuracy may be greatly influenced. To introduce the numerical dissipation for dispersion effect suppression, the governing equation of viscosity introduction is proposed as a minimum variation of conventional PD. Both the typical deformation in solids and the selective suppression on high frequencies are considered then the corresponding viscous force state is constructed. Finally, a numerical study is conducted to model the shock waves under extreme events and investigate the influence of wave discontinuity. It is indicated that the wave discontinuity aggravates the dispersion problem and shows Gibbs instability in the wave propagation. These can be effectively suppressed by the viscous force state, which verifies the proposed method. This provides an important reference to reproduce the correct wave propagation process and obtain the reasonable solid behavior in PD, thus helps to support and guide the research of national defense security field.

2023, 55(1): 134-147. doi: 10.6052/0459-1879-22-342

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TOPOLOGY DESIGN AND CHARACTERIZATION OF BROADBAND WAVE-SPLITTING METAGRATINGS FOR FLEXURAL WAVES

Li Lin, Zhang Xuebin, Liu Tao, Zhang Jun

Appearance of metasurfaces/metagratings makes anomalous control of wavefronts more and more convenient and flexible. However, most of the existing metasurfaces/metagratings are designed based on experience. As a result, their wavefront manipulation performance is often not optimal, and their working frequency bandwidth is narrow, which seriously limits their applications. Meanwhile, researchers found that as the incident angle is greater than a critical value, the generalized Snell’s law fails to estimate behavior of metasurfaces. In order to solve the above problems, based on the high-order diffraction theory, we propose a genetic optimization algorithm based method to design broadband wave-splitting metagratings. Based on the above technique, we specifically design three wave-splitting metagratings for flexural waves in thin plates, in which the supercells are composed of two subunits with a phase shift of $ {\text{π} } $. First, extensive numerical simulations are carried out to characterize the performance of our proposed metagratings and the optimized subunits. Then, a 3D printing technology is employed to fabricate metagratings and subunits to conduct experimental verification. Finally, our designed metagratings are compared with similar metagratings designed by two other methods. The results show that our metagratings work well as the designed functionality in the prescribed broad frequency range. However, the metagratings designed by two other methods only work well within a narrow frequency range. Although only flexural waves are considered in this work, our proposed technique is also applicable to other elastic waves. The results in this work provide a possible and effective way to design broadband metagratings for other waves.

2023, 55(1): 148-158. doi: 10.6052/0459-1879-22-373

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A TRUE TRIAXIAL CREEP CONSTITUTIVE MODEL FOR ROCK CONSIDERING HYDROCHEMICAL DAMAGE

Chen Youliang, Chen Qijian, Xiao Peng, Du Xi, Wang Suran

In order to accurately describe the characteristics of each stage of rock creep behavior under the combined action of acid environment and true triaxial stress, based on the chemical kinetic theory of water-rock interaction, a chemical damage factor considering pH and time is defined. The elastic body, nonlinear Kelvin body, linear Kelvin body, and visco-elastic-plastic body are connected in series, and the actual situation under the action of true triaxial stress is considered at the same time, a damage-creep constitutive model considering the coupling of rock acid corrosion and true triaxial stress is established. The parameters of the deduced model are identified and verified with the existing experimental research results. The yield surface equation of rock under true triaxial stress is obtained by data fitting, and the influence of intermediate principal stress on the creep model is discussed. The results show that the derived constitutive model can well reflect creep properties of the rock under acid corrosion The true triaxial creep characteristics under the action have certain rationality and practicability.

2023, 55(1): 159-168. doi: 10.6052/0459-1879-22-329

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DESIGN AND MODELING OF ELECTRET VIBRATION SUPPRESSION AND ENERGY HARVESTING DEVICE ORIENTED TO MICRO-VIBRATION SIGNALS

Liu Guoping, Yang Zhaoshu, He Zhongbo, Zhou Jingtao, Sun Minzheng

With the rapid development of space technology, and the continuous improvement of the processing precision requirements of advanced manufacturing, the control and utilization of low-frequency micro-vibration signals have attracted more and more attention. Using electret materials, we developed an integrated device to solve these problems, aiming to vibration suppression and energy harvesting, for low-frequency micro-vibration environments, and established the electromechanical coupling model of the electret vibration suppression and energy harvesting device, referring to the theory of dynamic vibration absorber (DVA). In order to meet the dual requirements of vibration suppression and energy harvesting, the influence of electrostatic force on the dynamic characteristics of the system was analyzed and equivalent, the parameters of the electret vibration suppression and energy harvesting device were evaluated and an optimization method for vibration suppression and energy harvesting was presented. We established a co-simulation environment of AMEsim and Simulink, and verified the model and results by simulation. The results of modeling and simulation showed that, the electromechanical coupling model of the electret energy harvesting device established in this paper can accurately describe its motion process, and the error of modeling and simulation is less than 5%. The vibration suppression and energy harvesting device is sensitive to the changes in parameters, and electrode spacing and stiffness of the secondary structure have stronger influence on the performance than the damping. Using our proposed optimization method for different usage scenarios, the device we designed can achieve the ability of ideal dynamic vibration absorber, or obtain 1700 V output voltage and 3.1 mW energy harvesting power sacrificing 15% of vibration suppression. The electromechanical coupling model and dynamic electrostatic force analytical model established in this paper are helpful to understand the working principle of the electret vibration suppression and energy harvesting mechanism, and reveal the change process and action mechanism of the nonlinear electrostatic force.

2023, 55(1): 169-181. doi: 10.6052/0459-1879-22-444

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THEORETICAL ANALYSIS ON THE CRITICAL FLOW VELOCITY AND VIBRATION MODE OF A TWIN-CHANNEL ROTATING PIPE

Zhang Bo, Zheng Haokai, Sun Dongsheng, Ding Hu, Chen Liqun

Rotating blade is an essential part of aero-engine. It serves in harsh conditions. Its failure is often caused by excessive vibration. To design the blade properly and to ensure the reliability and safety, the vibration characteristics of the blade need to be revealed. The blade is simplified as a cantilever rotating pipe with double cooling channels based on the Euler-Bernoulli beam theory. The influences of channel axis offset on fluid kinetic energy are considered in the present study. The motion governing equation of the blade is established including the bi-gyroscopic effects with the combination of Lagrange principle and assumed mode method. The method of order reduction and dimension expansion is applied to solve the eigenvalue of the system. The influences of the fluid velocity ratio, rotating speed, slenderness et al. on the first three order eigenvalue curves are studied. The present model degenerates into a simply supported pipe conveying fluid with a single channel to compare with the results reported in literature. The correctness of the present modeling method is verified, partly. The velocity ratio of two channels has great influence on the first three order critical flow velocity values. For a given value of the cross-section area of the cooling passage, the critical flow velocity of the twin-channel model is higher than the single-channel model. A circling phenomenon is introduced to on the second and the third eigenvalue curves by the gyroscopic effect due to the rotating motion. The second and the third eigenvalue curves travel through the imaginary axis several times. With the increase of the slenderness ratio, the system’s dynamic behaviors are similar to the non-rotating cantilever pipe. Moreover, due to the gyroscopic effect, the modal response of the lateral displacement presents a traveling wave property. And the damping factor has different enhancement or weakening effects on the first three modes under different parameter conditions.

2023, 55(1): 182-191. doi: 10.6052/0459-1879-22-456

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PERFORMANCE ANALYSIS AND STABILITY STUDY OF DIFFERENT TYPES OF NONLINEAR VIBRATION ABSORBERS WITH COMBINED STIFFNESS OF HORIZONTAL SPRINGS

Chen Yilin, Du Jingtao, Cui Haijian, Zhao Yuhao, Liu Yang

As a kind of vibration control unit, dynamic vibration absorber is widely used in various engineering situations, but the traditional linear vibration absorber can only achieve narrow band vibration control. On the basis of the linear vibration absorber, this paper introduces symmetrical horizontal springs to build a combined stiffness nonlinear vibration absorber with linear stiffness and nonlinear stiffness to improve the vibration absorption performance of the absorber. Considering the possible installation modes in actual projects, the combined stiffness nonlinear vibration absorber models of horizontal spring with grounding and without grounding are established respectively. The dynamic response is solved analytically by the harmonic balance method combined with the arc length continuation method, and the results are mutually verified with the numerical results, which proves the accuracy of the solution results. Then, the vibration absorption performance between two kinds of combined stiffness nonlinear vibration absorbers, the linear vibration absorber, and the nonlinear energy sink is analyzed and compared. It is found that the combined stiffness nonlinear vibration absorbers with horizontal spring grounding installation type not only retain the advantages of the linear vibration absorber, but also improve the shortcomings of its narrow vibration absorption frequency band. In addition, the combined stiffness nonlinear vibration absorber of horizontal springs grounding installation type has better vibration absorption performance in a wider frequency band near the main resonance frequency than the nonlinear energy sink. On this basis, the effects of horizontal spring parameters and absorber damping on the amplitude-frequency response and stability of the main structure are discussed. Finally, the complex dynamic behavior in the unstable region of the amplitude-frequency response curve of the main structure is observed and analyzed. The research results show that the appropriate design parameters can make the vibration peak value of the main structure low, and the unstable movement area of the frequency response curve is also small.

2023, 55(1): 192-202. doi: 10.6052/0459-1879-22-413

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DISCONTINUOUS BIFURCATIONS OF COEXISTING ATTRACTORS FOR A GEAR TRANSMISSION SYSTEM

Jin Hua, Lü Xiaohong, Zhang Zihao, Wang Xin

An important factor of rich dynamics in the gear transmission system is that there are a large number of various types of co-existing attractors. When multiple attractors coexist, the change of motion conditions and the inevitable disturbance may cause the gear transmission system to jump between different motion behaviors. As a result, the whole machine is adversely affected, and sometimes, the system structure will be destroyed. At present, some hidden attractors have not been found, and the bifurcation evolution characteristics of coexisting attractors have not been fully revealed. A single-degree-of-freedom spur gear system is considered. The Poincaré mapping compounded by local maps is constructed, and semi-analytic calculation method of eigenvalues of Jacobi matrix is presented. The stability and bifurcations of coexisting attractors are studied by applying numerical simulation, continuation shooting method and Floquet multipliers, and the basins of attraction of coexisting attractors are calculated by using cell mapping method. The influence of the meshing frequency, damping ratio and amplitude of time-varying excitation on the system dynamics is analyzed, and the discontinuous bifurcation behaviors including PD-type grazing bifurcation, saddle-node bifurcation induced by subcritical period-doubling bifurcation and boundary crisis are revealed in the gear transmission system. The saddle-node bifurcation induced by period-doubling bifurcation leads to the jump and hysteresis in the transition between adjacent periodic attractors, resulting in that the period-doubling bifurcation presents subcritical feature. The saddle-node bifurcation is a major factor for the appearance and disappearance of coexisting periodic attractors. The boundary crisis leads the chaotic attractor and its basin of attraction to disappear, and the bifurcation of corresponding periodic attractor terminates.

2023, 55(1): 203-212. doi: 10.6052/0459-1879-22-424

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EXTENSION-DECISION-BASED ADAPTIVE COLLISION AVOIDANCE CONTROL FOR VEHICLES

Chen Xiang, Cheng Shuo, Zhao Wanzhong, Wang Chunyan, Jiang Rui

Vehicle collision avoidance control can effectively avoid or mitigate vehicle collision accidents, which is one of the key control technologies of autonomous vehicles. Various traffic conditions, uncertain road adhesion coefficient and complex hydraulic brake execution system will reduce the effectiveness of collision avoidance control. Therefore, an adaptive collision avoidance control (ACAC) based on extension decision method is proposed in this paper. The control method is adaptive to the road adhesion coefficient and can accurately control the brake fluid pressure of the braking system. Firstly, the tire longitudinal force is estimated by the sliding mode observer (SMO), The designed SMO uses only the signal measured by sensors on board, i. e. the wheel angular speed to estimate the longitudinal tire force. Based on the observed tire longitudinal force, the road adhesion coefficient is estimated by the recursive least square method with forgetting factor (FFRL). Secondly, based on the estimated value of the road adhesion coefficient by FFRL, an ACAC method based on adaptive adjustment of road adhesion coefficient is proposed. This method determines which collision avoidance control strategy is adopted, that is, the extension decision method is used to judge whether short point braking, full braking or no braking. The impending collision time is defined as the main characteristic quantity, and the collision danger distance is the auxiliary characteristic quantity. A two-dimensional extension set is established based on the motion relationship between the ego vehicle and preceding vehicle and it can be divided into three different domains: the classical domain, the extension domain, and the non-domain. Thirdly, the effect of active deceleration control (ADC) is realized through precise hydraulic control by the executive system of electronic hydraulic braking system. Finally, the above methods are verified by manner of software joint simulation. The results show that the proposed algorithm has good collision avoidance effect in collision avoidance driving conditions.

2023, 55(1): 213-222. doi: 10.6052/0459-1879-22-347

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ADAPTIVE MULTI-FIDELITY POLYNOMIAL CHAOS-KRIGING MODEL-BASED EFFICIENT AERODYNAMIC DESIGN OPTIMIZATION METHOD

Zhao Huan

The multi-fidelity surrogate-assisted global aerodynamic optimization method has become one of the most efficient means to improve the efficiency and reliability of surrogate-based optimization algorithms. However, currently popular multi-fidelity surrogate models, e.g., co-Kriging and hierarchical Kriging (HK) models, lack the generalization ability and the adaptability to complex engineering applications, so that it is very difficult to promote them to be widely utilized. In this paper, based on the developed adaptive multi-fidelity polynomial chaos-Kriging (MF-PCK) surrogate model, an efficient global aerodynamic optimization framework based on the novel adaptive MF-PCK model is proposed while improving the modeling efficiency and the global approximation accuracy for highly-nonlinear and high-order response problems. In the development framework, we proposed a new adaptive multi-fidelity polynomial chaos-Kriging-based variable-fidelity expected improvement (MF-PCK-VF-EI) infilling strategy that can adaptively select new samples of both low- and high-fidelity, which further improves the efficiency and ability of this optimization framework. The developed methodology is verified by one analytical function example and demonstrated by three engineering application problems, including the deterministic optimization and the robust design optimization of several transonic aerodynamic shapes, compared with the popular Kriging-based and HK-based optimization algorithms. The results show that the global aerodynamic optimization efficiency of the developed method based on the novel adaptive MF-PCK model is higher than that based on the HK model and more than twice that based on the Kriging model, meantime with better and more reliable results. More importantly, the efficiency and performance of robust aerodynamic design optimization (RADO) for transonic aerodynamic shapes are prone to satisfy the requirements for complex engineering applications, which proves a significant advantage of the developed method over the popular Kriging-based and HK-based optimization algorithms.

2023, 55(1): 223-238. doi: 10.6052/0459-1879-22-391

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INVESTIGATION OF THE TIME EFFICIENCY OF THE SEVENTH-ORDER WENO-S SCHEME

Wu Conghai, Li Hu, Liu Xuliang, Luo Yong, Zhang Shuhai

The WENO-S scheme is a class of weighted essentially non-oscillatory schemes suitable for numerical simulations of problems with discontinuities. The smoothness indicator of this kind of scheme is constant for single-frequency waves, which makes this kind of scheme have exactly the same approximate dispersion relationship with its linear base scheme, and thus has an excellent ability to simulate small-scale waves. Time efficiency is crucial for numerical methods. For a WENO-S scheme, the formula of the smoothness indicator on each sub-stencil has the same formula except for different subscripts. Then some smoothness indicators are the same when calculating adjacent numerical fluxes of linear convection equations. So, a method is proposed to remove redundant computations of smoothness indicators. The premise of this approach is that the quantity used for reconstruction or interpolation on a grid line can be represented as a sequence. According to this requirement, the feasibility and application requirements for several different physical problems are analyzed. The seventh-order WENO-S scheme is employed to illustrate the advantages of the WENO-S schemes, including good properties near extreme points, good stability near discontinuities, and outstanding spectral properties. Then the method of eliminating the computation of the redundant smoothness indicators is introduced. In numerical computation, all smoothness indicators in a grid line are calculated and stored in advance. With this approach, the count of the smoothness indicator calculation is about 1/4 of the original one for the seventh-order WENO-S scheme when there are many grid points. Numerical examples include one-dimensional advection, spherical wave propagation, two-dimensional rotation, small disturbance propagation, and one- and two- dimensional inviscid flow problems. The numerical results show that this scheme can capture a variety of flow structures well and have good time efficiency. Furthermore, the proposed method reduces the computational time by about 20%.

2023, 55(1): 239-253. doi: 10.6052/0459-1879-22-371

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A SCALE-INVARIANT HIGH-ORDER WCNS SCHEME

Zhang Zixuan, Dong Yidao, Huang Ziquan, Kong Lingfa, Liu Wei

For numerical simulation of high-speed flows, it requires that small-scale structures are resolved with high-fidelity, and discontinuities are stably captured without spurious oscillation. These two aspects put forward almost contradictory requirements for numerical schemes. The widely used high-order schemes can satisfy the two demands required above to some extent. However, they all have advantages and disadvantages compared to each other and no one can be considered perfect. For example, high-order schemes are prone to generating numerical oscillations near discontinuities when a small-scale problem is discretized, such as the Reynolds-stress model. To solve this deficiency, a simple, effective and robust modification is introduced to the seventh-order weight compact nonlinear scheme (WCNS) by making use of the descaling function to formulate a scale-invariant WCNS scheme. The descaling function is devised using an average of the function values and introduced into the nonlinear weights of the WCNS7-JS/Z/D schemes to eliminate the scale dependency. The design idea of the scale-invariant WCNS scheme is to make weights independent of the scale factor and the sensitivity parameter. In addition, the shock-capturing ability of the new scheme performs well even for small-scale problems. The new schemes can achieve an essentially non-oscillatory approximation of a discontinuous function (ENO-property), a scale-invariant property with an arbitrary scale of a function (Si-property), and an optimal order of accuracy with smooth function regardless of the critical point (Cp-property). We derive the seventh-order D-type weights. The one-dimensional linear advection equation is solved to verify that WCNS schemes can achieve the optimal (seventh) order of accuracy. We test a series of one- and two-dimensional numerical experiments governed by Euler equations to demonstrate that the scale-invariant WCNS schemes perform well in the shock-capturing ability. Overall, the scale-invariant WCNS schemes provide a new method for improving WCNS schemes and solving nonlinear problems.

2023, 55(1): 254-271. doi: 10.6052/0459-1879-22-399

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METHODS AND APPLICATIONS OF PHYSICAL INFORMATION DEEP LEARNING IN WAVE NUMERICAL SIMULATION

Chen Su, Ding Yi, Sun Hao, Zhao Mi, Wang Jinting, Li Xiaojun

In recent years, physics-informed deep learning methods based on prior data fusion to solve forward and inverse problems based on partial differential equations (PDEs) have become a cross-disciplinary hotspot. This paper clarifies the mathematical concept and implementation of physics-informed neural networks (PINN) for the earthquake engineering numerical simulation of waves. Taking the one-dimensional fluctuation of passive term as an example, the relevant theoretical model of PINN is constructed. The feasibility of physics-driven deep learning methods in solving fluctuation problems is verified by comparing with analytical solutions and finite difference methods. The relative $ {\mathcal{L}}_{2} $ norm errors of the wave field simulated by PINN method and other numerical algorithms are analyzed. The physical driven deep learning method combined with sparse initial wave field data formed by spectral element method is used to numerically simulate two-dimensional fluctuation problem. Typical working conditions such as free boundary conditions and undulating ground surface are realized, and the distribution characteristics of time series wave field are given. Different initial conditions are changed to test the generalization accuracy of the neural network, and a transfer learning method was proposed to significantly improve the training efficiency of the network. By using transfer learning, wave fields at different source locations in infinite media can be directly predicted with high accuracy. Comparing with the results of spectral element method, the reliability of the proposed method is verified to simulate the wave propagation of homogeneous site, spatial inhomogeneity and complex terrain site fluctuation. The results show that the physical-driven deep learning method has the advantages of meshless and fine-grained numerical simulation, and can realize the numerical simulation conditions such as free surface and side/bottom boundary wave field transmission.

2023, 55(1): 272-282. doi: 10.6052/0459-1879-22-401

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2023, 55(1): 283-284.

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2023 Vol. 55, No. 1

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