力学学报

PROGRESS IN THE RESEARCH OF HYPERSONIC AND HIGHENTHALPY BOUNDARY LAYER INSTABILITIES AND TRANSITION

Chen Xianliang, Fu Song

Boundary layer transition from laminar to turbulence is of vital importance to the design of hypersonic vehicles. With continuous expansion of flight speed and altitude domains, the high-temperature gas effects in hypersonic high-enthalpy boundary layers invalidate the calorically perfect gas assumption. They can thus largely influence the flow transition process. Relevant research is multi-interdisciplinary and multi-physics coupling. In recent years, the hypersonic high-enthalpy boundary layer transition has received increasing interest worldwide owing to rapid development of vehicle design. Recent progress is reviewed in this article. Firstly, commonly used high-temperature gas models are introduced, especially the thermochemical non-equilibrium models. Then, the prevailing computational methods for high-enthalpy flows, including the shock-capturing, shock-fitting and boundary layer equation methods are introduced. The progress in experimental techniques for high-enthalpy wind tunnels and flight tests are also summarized. Afterward, the influences of high-temperature effects on the receptivity, modal growth, transient growth and nonlinear interactions in the transition process are reviewed. Here some phenomena has received wide interests that the third mode and the supersonic mode appear at relatively large growth rates in the streamwise instability. Finally, the progress is summarized, and future researches are briefly prospected.

2022, 54(11): 2937-2957. doi: 10.6052/0459-1879-22-184

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IMPACT OF A PLANAR SHOCK ONTO SIDE-BY-SIDE DROPLETS: A 3D NUMERICAL STUDY

Wu Runlong, Li Zhujun, Ding Hang

In this paper we investigate the evolution dynamics of side-by-side droplets after being impacted by a planar shock by using a three-dimensional conservative sharp interface method. Our research mainly focuses on the development of wave structures after the shock impact and the asymmetric interface evolution of single droplet induced by the coupling between the side-by-side droplets. Firstly, we analyze the development of the wave system including those inside and outside the channel between the side-by-side droplets. We find that at the early stage of impact, the intersection of reflected shock waves accounts for the formation of new reflected shock waves and Mach rods. This is quite different from the curved wave front formed by the reflected shock wave on the other side of the droplet transversely opposite to the channel. The difference of the flow field on the two sides of the droplet is responsible for the asymmetric interface evolution of the droplet in the middle stage of the droplet-shock interaction. Secondly, we investigate the interface morphology and its evolution in the middle stage of shock impact, especially when the incident shock wave moves to the downstream of and is far away from the droplets, and report the occurrence of new flow phenomena at the downstream outlet of the channel, such as interface coalescence caused by airflow expansion and subsequent interface fragmentation owing to airflow blockage. Finally, the effect of the gap between the side-by-side droplets on the droplet interaction is studied. We find that the gap size has a significant effect on the occurrence of pressure peaks in the channel. Specifically, a smaller gap not only brings higher pressure peak, but also makes the peak appear at an earlier time.

2022, 54(11): 2958-2969. doi: 10.6052/0459-1879-22-358

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ACTIVE FLOW CONTROL OF WAVY CYLINDER BASED ON STEADY BLOWING AND SUCTION

Zou Lin, Zuo Hongcheng, Liu Diwei, Wang Jiahui, Xu Jinli

Based on the control of the near wake flow of a wavy cylinder by steady blowing and suction to enhance the vibration of the cylinder, the effects of the forward blowing and backward suction and the forward and backward suction control modes on the lift and drag characteristics, time-average pressure coefficient, circulation, turbulent kinetic energy and flow field mechanism of a wavy cylinder under different blowing and suction conditions at subcritical Reynolds number (Re = 3000) were numerically studied by large eddy simulation. It is found that the fluctuating lift coefficient of wavy cylinder under the control of forward blowing and backward suction and forward and backward suction is significantly increased under different conditions of blowing and suction momentum coefficient, and the maximum increase is as high as 636% and 391% respectively compared with that of uncontrolled cylinder and wavy cylinder. This may be mainly attributed to the shorter recirculation area of wavy cylinder under the control of blowing and suction, the concentration of high-intensity vortices towards the rear of blunt body, and the shorter vortex formation length, The "riblike vortex" formed by the interaction of spanwise vortex and streamwise vortex becomes larger and longer, and the normalized circulation near the wake increases significantly, resulting in the increase of fluctuating lift coefficient, which may lead to stronger vibration of the cylinder; At the same time, both control methods change the pressure distribution on the surface of the wavy cylinder. Because the front end tends to be streamlined due to the blowing at the front stagnation point of the wavy cylinder, the high-pressure area of the wavy cylinder decreases under different blowing and suction momentum coefficients, but the low-pressure area increases due to the suction at the rear stagnation point, while the high-pressure area of the wavy cylinder is basically unchanged and the low-pressure area increases under different blowing and suction momentum coefficients. The research results can provide basic theoretical support for improving the efficiency of distributed wind energy capture structure in low wind speed areas.

2022, 54(11): 2970-2983. doi: 10.6052/0459-1879-22-212

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STUDY OF THE TEMPORAL-SPATIAL FLUCTUATIONS AND EMPIRICAL MODEL OF NEAR SPACE ATMOSPHERIC DENSITY

Zeng Dandan, Wan Tian, Li Shuaihui

Atmospheric density is a fundamental parameter for vehicle designing and flight controlling. In recent years, many researchers have discovered that atmospheric densities in the upper mesosphere and lower thermosphere predicted by the empirical model, such as USSA-76 and NRLMSISE-00, are larger than the measured values. On the other hand, vehicle designing is tending to be more detailed, and engineers hope that the empirical models provide densities under variable latitudes, day-night times and seasons. Based on that, the present work analyzesdependences of near-space atmospheric density on latitude, solar local time and date, by using satellite observed data. Emphasizes are put on density fluctuation patterns and amplitudes. The fluctuation patterns caused by latitude and date vary with altitude, and the amplitudes are largest at 78 km and locally smallest at about 22 km and 92 km. The fluctuation amplitude caused by the solar local time increases monotonically with altitude. Based on the temporal-spatialfluctuationlaw, we proposed the temporal-spatial fluctuation modelfor the near-space atmospheric density, which describes the density fluctuations with latitude, local time and date. The present model describes the temporal-spatial fluctuations better than the existed empirical models at variable altitudes. The confidence coefficient of the present model is much better than NRLMSISE-00 under the same error band. The modeling method in this work is reasonable, and the obtained model could be used in near-space vehicle designing.

2022, 54(11): 2984-2993. doi: 10.6052/0459-1879-22-231

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FLUID FLOW AND HEAT TRANSFER CHARACTERISTICS IN THE MULTILAYERED-PARALLEL FRACTURED POROUS CHANNEL

Li Qi, Wang Zhaoyu, Hu Pengfei

Based on the Brinkman-extended Darcy model and the local thermal equilibrium model, the fluid flow and heat transfer characteristics in the multilayered-parallel fractured porous channel are studied. The analytical solutions of velocity field, temperature field in each region of multilayered-parallel fractured porous channel, friction coefficient and Nusselt number are obtained. The effects of the fracture number, Darcy number, hollow ratio and the ratio of effective thermal conductivity on heat transfer characteristics are analyzed. The results show that when Darcy number is small, the Darcy velocity in the porous media which does not change with the porous height increases with the increase of the number of fracture layers, and is not affected by the porous layer position in multilayer porous channel with certain number of fractures. Increasing the number of fracture layers weakens the influence of hollow ratio on pressure drop and increases the fluid pressure drop in the channel, but the increase degree gradually decreases. The increase of the ratio of effective thermal conductivity or decrease of the hollow ratio leads to a stepwise temperature distribution in the multilayered fractured porous channel, while the temperature distribution curves in the multilayered fractured channel tend to be consistent when the thermal conductivity ratio is small or the hollow ratio is large. Furthermore, when the ratio of thermal conductivity is small, the heat transfer effect in multilayered fractured porous channel is better than that in single fractured porous channel at any hollow ratio. However, when the ratio of thermal conductivity is large, there is a critical hollow ratio, which makes the heat transfer effect in the channels with different numbers of fracture layers be the same, and increasing the number of fractured layers has little influence on the heat transfer effect in multilayered fractured porous channel.

2022, 54(11): 2994-3009. doi: 10.6052/0459-1879-22-285

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A HIGH-EFFICIENCY AND HIGH-RESOLUTION MAPPED WENO SCHEME AND ITS APPLICATIONS IN THE NUMERICAL SIMULATION OF PROBLEMS WITH COMPLEX FLOWS

Zhong Wei, Jia Leiming, Wang Shufei, Tian Zhou

The traditional mapped weighted essentially non-oscillatory (WENO) schemes commonly suffer from the drawback of low-efficiency, since they usually require the mapping processes resulting in extra computational costs. The goal of the present work is to improve the efficiency of the mapped WENO schemes. By designing a set of approximate constant mapping function which is devised using an approximation of the standard signum function, a novel mapped WENO scheme is proposed. The new mapping function is devised to meet the overall criteria for a proper mapping function required in the design of the WENO-PM6 scheme. The WENO-PM6 scheme was presented to overcome the potential loss of accuracy of the well-validated WENO-M scheme in previously published literature. The new proposed mapped WENO scheme is denoted as WENO-ACM. It maintains almost all advantages of the WENO-PM6 scheme, such as low dissipations and high resolutions. However, it decreases the number of mathematical operations remarkably in every mapping process leading to a significant improvement of efficiency. Theoretical analysis indicates that the new scheme can attain the optimal convergence rate of accuracy regardless of critical points. The investigation of approximate dispersion relation (ADR) shows that the spectral properties of the new scheme are significantly improved. A variety of benchmark-test problems, including accuracy tests, standard shock-tube problem, Mach 3 shock-entropy wave interaction, Woodward-Colella interacting blast waves, 2D Riemann problem, double Mach reflection, forward-facing step problem, Rayleigh-Taylor instability and Kelvin-Helmholtz instability are conducted. Compared to the well-established WENO-JS, WENO-M, WENO-PM6 schemes comprehensively, the present scheme exhibits significantly improved high efficiency, very high resolution and sharp discontinuity capturing. Most importantly, the extra computational cost of WENO-ACM compared to WENO-JS is much lower than those of WENO-M and WENO-PM6. Specifically, WENO-ACM can reduce the extra computational cost compared to WENO-JS more than 80% and 90% against WENO-M and WENO-PM6, respectively.

2022, 54(11): 3010-3031. doi: 10.6052/0459-1879-22-247

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VORTEX IDENTIFICATION TECHNOLOGY AND ITS APPLICATION IN THE WAKE FIELD OF MARINE PROPELLER

Yang Lin, Zheng Xing

Vortex identification is a very important problem of fluid and flow, in order to find a reasonable method of vortex identification in the wake of marine propeller, this paper studies the theory of six kinds of vortex recognition technology combined with practice, in which analytic solutions of both Burgers vortex and Lamb-Oseen vortex are also used for necessary explanation. The advantages and disadvantages of various vortex identification methods are discussed in detail at the angle of theory and application. The local low-pressure criterion is intuitive, but it is obviously insufficient after considering viscous and unsteady effects. The path line or streamline criterion obviously cannot satisfy Galileo invariance, which will cause confusion in vortex identification. The magnitude of vorticity criterion needs to specify its threshold value, which has certain uncertainty, and can also incorrectly identify vortex sheets that are not vortices. The complex eigenvalue of the velocity gradient tensor will also have an unrecognized region. The second invariant criterion of the velocity gradient tensor and the second eigenvalue criterion of the symmetric tensor can better identify the vortex core, and these two criteria are sometimes equivalent. The numerical simulation of propeller wake is implemented on the open source software OpenFOAM platform. The large eddy model is modeled by a local dynamic equation, which is better than the dynamic Smagorinsky model to a certain extent. The results of numerical experiment show that, for the vortex identification in the marine propeller wake, the second invariant criterion of the velocity gradient tensor is consistent with the second eigenvalue criterion of the symmetric tensor. However, the local minimum pressure criterion, streamline or path line criterion, vorticity magnitude criterion and complex eigenvalue criterion of velocity gradient tensor have some defects, which are not suitable for vortex identification in the wake of marine propeller.

2022, 54(11): 3032-3041. doi: 10.6052/0459-1879-22-339

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EXPERIMENTAL STUDY ON EVOLUTION OF WAKE STRUCTURES IN FLOW PAST THE CIRCULAR CYLINDER PLACED NEAR THE WALL

Qiu Xiang, Wu Haodong, Tao Yizhou, Li Jiahua, Zhou Jiankang, Liu Yulu

The experimental measurement of the flow field around the circular cylinder near the wall is carried out by using the Particle Image Velocimetry. The characteristics of the flow regime under different Reynolds numbers (${Re} = {1500} \sim {5540}$) together with three different gap ratios (${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 0}{.5}$, ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{\; = 1}{.0}$, ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 1}{.5}$) are studied. The experiment results shows that for the case of ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 0}{.5}$, with the increasing of Reynolds number, the recirculation zone behind the cylinder is gradually symmetrical about the centerline of the cylinder while its size is decreasing, and the size of the separation bubble on the wall also decreases gradually. The experiment reveals that the cylindrical wake and the gap flow perform differently while the Reynolds numbers ${{Re} _t}$ between ${Re} = {3000} \sim {3200}$. When the Reynolds number is smaller than ${{Re} _t}$, a small separation bubble will form on the front wall of the cylinder, which hinders the flow of upstream fluid through the gap and reduces the intensity of the gap flow, and then deviates from the wall. At ${Re} { \;= 1500}$, the vortex shedding frequency increases with the decrease of the gap ratio. And with the decrease of gap ratio, the vortex shedding frequency increases first and then decreases in a small range (${0}{.185} \leqslant St \leqslant {0}{.227}$) for ${Re} \geqslant {3000}$. The Reynolds number has a significant influence on the flow characteristics, especially for the case of small gap ratios. At ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 0}{.5}$, the secondary vortex deviates from the wall and moves upward to the position close to the upper wake vortex, and the vortex merging process appears between the upper wake vortex and the secondary vortex for the ${Re} { \;= 1500}$. As the Reynolds number increases to ${Re} { \;= 5540}$, the secondary vortex does not merge with the upper wake vortex, and the secondary vortex directly interacts with the lower wake vortex. At ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 1}{.0}$ and ${G \mathord{\left/ {\vphantom {G D}} \right. } D}{ \;= 1}{.5}$, the energy carried by the secondary vortex is decreasing gradually with the increasing of Reynolds number.

2022, 54(11): 3042-3057. doi: 10.6052/0459-1879-22-403

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STRESS RELAXATION DYNAMICS FOR AMORPHOUS ALLOYS BASED ON THE EVOLUTION OF MICROSTRUCTURAL HETEROGENEITY

Hao Qi, Qiao Jichao

The correlation between stress relaxation behavior and the evolution of microstructural heterogeneity of Zr-based amorphous alloys was probed. Amorphous alloy is the typical non-equilibrium solid system. Stress relaxation process is accompanied by aging effect of the amorphous alloy. In the current work, the coupling evolution of the most probably characteristic time $\tau $ and stretched exponent $\;\beta $ in the classical stretched function is considered for the first time, indicating the time dependence of structural state in the stress relaxation process. Based on the evolution of the non-equilibrium structure state of the amorphous alloys, the aging effect in the stress relaxation behavior was clarified. The results demonstrated that the stress relaxation behavior of amorphous alloys has non exponential characteristics. The exponential relaxation form of single characteristic time and the finite spectrum method of finite characteristic time cannot describe accurately the experimental results. This phenomenon is ascribed to the continuous distribution of the characteristic time spectrum caused by the microstructural heterogeneity of amorphous alloys. In addition, the stress relaxation behavior in the apparent elastic region is independent of the initial strain, which is due to the macroscopic flow nature of the stress relaxation behavior. Elastic and anelastic reversible deformation is transformed into viscoplastic (irreversible) deformation. Finally, Evolution of structural parameters caused by aging during stress relaxation is considered, which is reflected in the increase of characteristic time $\tau $ and the decrease of stretched exponent $\;\beta $.

2022, 54(11): 3058-3067. doi: 10.6052/0459-1879-22-255

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ANALYTICAL SOLUTION OF STATICALLY INDETERMINATE BEAM-COLUMN

Li Yinshan, Ding Qian, Li Zirui, Guo Chunxia, Sun Yongtao, Liu Zhanli

In this paper, the problem of statically indeterminate beam-column bending is studied by using the asymptotic integral method. Firstly, the fourth order deflection differential equation of statically indeterminate beam-column is established. Considering the boundary condition and continuous smooth condition, the exact analytical solution of the deflection is obtained by using continuous piecewise independent integration method. In order to meet the requirements of engineering design, the statically indeterminate beam-column of the fourth order equation is constructed. The deflection line of statically indeterminate beam without axial force is selected as the initial function of beam. The initial function is substituted into the fourth-order deflection differential iterative equation of the beam for integration. The boundary condition and continuous smooth condition are used to determine the integral constant to get the next iteration deflection function. The iterative integral operation is carried out in turn. The polynomial analytical function solutions of the maximum deflection, the maximum angle and the maximum bending moment expressed by the axial force amplification coefficient are calculated. The statically indeterminate beam-column subjected to distributed forces under two boundary conditions are analyzed in this paper. The calculation results show that when the axial force of statically indeterminate beam-column is less than half of Euler critical force, the error can be controlled within 1% after six iterations. Not only the beam-column’s maximum displacement and shear force increase with the increase of axial force, but also the position of the maximum displacement and internal force migrate with the increase of axial force. The research in this paper is of great significance to reveal the influence of axial force on statically indeterminate beam-column deformation and internal force, and provides a certain theoretical basis for the practical design of statically indeterminate beam-column.

2022, 54(11): 3068-3079. doi: 10.6052/0459-1879-22-337

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DISCUSSION ON BOUNDARY VALUE PROBLEMS OF A MINDLIN PLATE BASED ON THE SIMPLIFIED STRAIN GRADIENT ELASTICITY

Xu Xiaojian, Deng Zichen

It is reported from both the experiments and molecular dynamics that the materials and structures will exhibit a remarkable size-effect when their characteristic sizes shrink down to the micro- to nano-scales. Therefore, it is a hot topic of current interest in the research communities that whether is it possible to establish an accurate continuum model that is capable of predicting the mechanical behaviors of materials and structures. Although numerous studies have been carried out on the mechanical behaviors of Mindlin plates, their variationally consistent boundary value problems and the related issues have not been well addressed in the open literature. Firstly, the strain energy of an isotropic Mindlin plate within the context of the simplified strain gradient elasticity is given. Then, the variationally consistent boundary value problems of the Mindlin plate model and the corresponding corner conditions in terms of displacement derivations are derived using the variational principle and tensor analysis. It is verified that the present boundary value problems of the Mindlin plate model recover to the corresponding boundary value problems of the Timoshenko beam model and Kirchhoff plate model. It is found that the governing equation of the transverse behavior of the present Mindlin plate model involves a set of a decoupled twelfth-order partial differential equation, and therefore, should enforce six boundary conditions on each plate side, to constitute a well-posed boundary value problem. The possible boundary conditions of a circular plate and a rectangular plate are discussed. The corner conditions, produced by the double stresses, are closely related to normal gradients of classical components of the shear force, the bending moment and the twisting moment. The corner conditions, existed in the present Mindlin plate model, are firstly clarified. The present work is expected to be a useful tool for developing effective numerical methods, such as the finite element method and the Garlerkin method.

2022, 54(11): 3080-3087. doi: 10.6052/0459-1879-22-310

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BENDING PERFORMANCE ANALYSIS OF FLEXOELECTRIC NANOPLATE CONSIDERING ELECTRIC FIELD GRADIENTS

Cao Caiqin, Chen Jingbo, Li Dongbo

The size-dependent flexoelectric effect plays an increasingly critical role in the design of smart devices. Researchers have done much work in multi-physics field analysis at the micro- or nano-scale. The electromechanical coupling behavior of nanoplate in the bending problem is analyzed based on the non-classical theory of elastic dielectric materials considering the flexoelectric effect and electric field gradient effect, using two-dimensional nanoplate as an example. The Mindlin assumption is used to obtain the first-order truncation of the displacement field and electric potential field of the Mindlin plate, the material of plate is assumed to be a cubic crystal in m3m class, the two-dimensional constitutive equations are obtained by substituting the three-dimensional constitutive equations into the expressions of higher-order stress, higher-order couple stress, higher-order electric displacement and higher-order quadrupole, the governing equations of the plate and the line integral equation on the boundary are simultaneously derived through the elastic dielectric variational principle, hence the higher-order bending equations, the higher-order electric potential equation, and the corresponding simply-supported boundary conditions of the rectangular plate are obtained by substituting the two-dimensional constitutive equations and the directional cosine on the boundary into the governing equations of the plate and the line integral equation on the boundary, respectively. According to the higher-order bending equations, higher-order electric potential equation, the corresponding simply-supported boundary conditions of rectangular plate, and the Navier solution theory, the electric potential field of nanoplate are analytically solved, with a focus on the influence of electric field gradient effect on the electric potential in the plate. The numerical results show that the electric field gradient weakens the first-order electric potential generated by the flexoelectric effect in the nanoplate, and the greater the material parameter g₁₁, the greater the weakening of the first-order electric potential. In addition, the existence of the electric field gradient eliminates the singularities of the first-order electric potential of nanoplate under transverse concentrated loading. Present work can be seen as an extension of the structural analysis theory of nanoplate with flexoelectric effect and electric field gradient effect, which provides a reference for the structural design of micro- or nano-scale devices.

2022, 54(11): 3088-3098. doi: 10.6052/0459-1879-22-282

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PROPERTY PREDICTION METHODS OF GRANULAR SOIL PENETRATION GROUTING REINFORCED BODY BASED ON FRACTAL THEORY AND MORI-TANAKA METHOD

Peng Peng, Peng Feng, Sun Zhenyu, Zhang Dingli

In the grouting reinforcement project, in order to avoid the instability of the support structure due to excessive force caused by spatial variability, a reasonable prediction method for the stiffness and strength of grouting reinforced body is necessary. The fractal theory is used to describe the pore characteristics of the granular soil type tunnel surrounding rock, and the conversion relationship between the body porosity and surface porosity of the surrounding rock is established based on the empirical formula of tortuosity. A new macroscopic stiffness prediction method for grouting reinforced body is proposed based on the Mori-Tanaka method with the body porosity as the variable. By using energy method to solve the bulking critical load of different half-wave distribution patterns of connecting pores as the uniaxial compressive strength of the grouting reinforced body, so that a new theoretical model for strength prediction of grouted reinforced body is established. The Yujingshan tunnel is used as the engineering background, the method proposed by this paper is secondly developed in FLAC^3D, by randomly generating porosity for different surrounding rock elements, the mechanical properties calculated by proposed stiffness and strength prediction methods of grouting reinforced body is assigned to the surrounding rock elements, and the spatial variability of surrounding rock is realized. The maximum absolute error of the horizontal convergence of the tunnel between simulation and monitoring result is only 8 mm. The numerical simulation results show that the grouting reinforcement of the backfill region of Yujingshan tunnel can reduce the surrounding rock displacement by 50%-90%, greatly reduce the bending moment of support structure corresponding to surrounding rock region which has poorly physical and mechanical properties, reduce the support structure torque to 0, and control the support deformation within 10 mm. However, the load distribution law between the backfill region and limestone cannot be changed by grouting.

2022, 54(11): 3099-3112. doi: 10.6052/0459-1879-22-308

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EQUATION AND NUMERICAL SIMULATION ON MULTISCALE STRESS RESPONSE OF CONCRETE

Li Xiangnan, Zuo Xiaobao, Zhou Guangpan, Li Liang

Aiming at the multi-phase and multi-scale composition characteristics of concrete and its complicated mechanical response problem, firstly, according to the geometric characteristics of constituent material in concrete, C-S-H gel, hardened cement paste, cement mortar and meso-scale concrete were respectively regarded as composite materials at different scales of concrete, including the nanoscale, microscale, sub-mesoscale and mesoscale, and their simplified geometric models were reconstructed by using the particle space accumulation method. Secondly, based on the reconstructed simplified geometric model and equivalent inclusion theory, the transition relationship of stress response between composite materials at different scales of concrete was established by using upscaling calculation method of equivalent stiffness and downscaling calculation method of stress response, on this basis, the multiscale stress response equation of concrete under the loading was derived, and the corresponding computing program was compiled. Finally, taking the uniaxial compressive loading as an example, the stress response in composite materials at different scales of concrete under uniaxial compressive loading was numerically calculated, and the influence of spatial position and interaction of aggregate particles, as well as the stiffness, geometric shape and spatial orientation of cement hydration products on their stress response were analyzed. Results show that, the stress distribution in the meso-scale concrete is uneven under uniaxial compressive loading, which was affected by the distance between the aggregate particles, and the effective impact range is about 6 times the radius of aggregate particle. The stiffness, geometric shape and spatial orientation of cement hydration products are important factors affecting their stress distribution under loading, the greater the stiffness, the greater the stress in the hydration products, while the smaller the angle with the direction of loading, the greater the stress in the hydration products of prolate ellipsoids along this direction, however, the stress in the hydration products of oblate ellipsoids is the opposite.

2022, 54(11): 3113-3126. doi: 10.6052/0459-1879-22-269

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COLLABORATIVE DYNAMICS TOPOLOGY OPTIMIZATION OF COMBINED STRUCTURE

Wen Ming, Wang Dong

An engineering structure is usually composed of multiple components for carrying loads. Between them, the loads or vibration energies are transferred through the linkage members. Then, the layout and properties of the linkage members have a great influence on the topological configuration, mechanical performance and load-bearing capacity of the entire structure. In this paper, the collaborative dynamic topology optimization of the configuration of the combined structure and the layout of the linkage members between components is studied. A spring connection element is employed to represent the linkage member for its restraint behaviors. With the constraints of the material usage and the linkage member number, the dynamic compliance of the entire structure is pursued for minimization under the external harmonic excitation. By taking the relative material densities of the load-bearing members and the relative stiffness of the spring connecting elements as the design variables, the topological configuration of the combined structure and the layout of the linkage members are optimized collaboratively with use of the gradient-based optimization algorithm. By comparison with the optimal topology designs of the integral structures without linkage members, the topological configuration changes of the combined structure and the influences of the layout of the linkage members are illustrated on both the overall material distribution and dynamic properties. In addition, the dynamic topology optimization of the combined structure is implemented with the linkage members subjectively arranged. Numerical results show that the dynamic compliance of the collaborative optimization results for the combined structures are always greater than the equivalent integral structures. However, the variations of the structural natural frequencies of the combined structures are usually unpredicted mainly due to the changes of the corresponding mode shapes, which can provide a more superior structural configuration and connection layout in the process of the conceptual design stage of a practical structure.

2022, 54(11): 3127-3135. doi: 10.6052/0459-1879-22-292

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STUDY ON VIBRATION REDUCTION OF DYNAMIC VIBRATION ABSORBER FOR TWO-SCALE DUFFING SYSTEM

Wan Honglin, Li Xianghong, Shen Yongjun, Wang Yanli

Duffing system with two-scale coupling generally will behave in complex vibration, because of the characteristics of large amplitude and high frequency, then the harm from complex vibration cannot be ignored. The vibration control problem of linear vibration absorber for Duffing system with low frequency parameter excitation is studied. By comparing the time history diagram and phase diagram of the system before and after coupling the linear dynamic vibration absorber, the system with dynamic vibration absorber shows mixed vibration mode (bursting vibration), and the vibration amplitude is suppressed significantly, especially for the high frequency vibration part. Using the slow-fast analysis method, the corresponding autonomous system is obtained when the parameter excitation is a slowly varying process. It is found that the stability and bifurcation behavior of the autonomous system can obviously regulate the vibration response of the non-autonomous system. The results show that although fork bifurcation occurs in the autonomous system before and after the coupled dynamic vibration absorber, the stability of the autonomous system changes after the dynamic vibration absorber is added. Comparing to the stable center in the original system, the attractor of the autonomous system coupled linear dynamic vibration absorber changes to asymptotically stable focus. The attractive force of the stable equilibrium line of autonomous system to trajectory of non-autonomous system is enhanced, which reduces the vibration amplitude of the non-autonomous system. In addition, the reduction about hops times of trajectory between different attractors is another reason for the decrease of the vibration amplitude. Based on the analysis of vibration reduction effect with relevant parameters of parametric excitation, it is found that the dynamic vibration absorber can suppress the vibration of the system in a large vibration amplitude and frequency range. It provides a theoretical basis for the research on vibration reduction of two-scale system coupled linear dynamic vibration absorber.

2022, 54(11): 3136-3146. doi: 10.6052/0459-1879-22-286

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THEORETICAL AND EXPERIMENTAL STUDY ON VORTEX-INDUCED VIBRATION SUPPRESSION BASED ON NONLINEAR TARGETED ENERGY TRANSFER

Lu Zi, He Yixiang, Zhang Lanbin, Dai Huliang, Wang Lin

Flow-induced vibration of the structure widely occurs in many important engineering fields such as mechanical, aerospace, civil and petroleum. In order to prevent fatigue and failure of the engineering structures due to flow-induced vibrations, it’s necessary to do deep researches on stability, dynamic responses and vibration controls. In this paper, a nonlinear targeted energy transfer (NTET) model composed of linear springs and mass block is proposed. The passive control mechanism of nonlinear energy absorbers on the vortex-induced vibration of an elastically supported cylinder is investigated. Firstly, based on the energy method, the coupling dynamic equations for the nonlinear passive control on vortex-induced vibration of a cylinder are established. Then, experimental study is conducted by designing the nonlinear spring-mass configuration of NTET. Good agreements are obtained by comparing experimental results with theoretical predictions. Finally, the optimal parameters of the NTET for improving the control performance of vortex-induced vibrations are obtained. It is found that some NTET parameters such as mass, spring stiffness and spring prestress have significant impacts on the control performance. The results show that both the cylinder and NTET exhibit periodic steady-state vibration responses. Changes in the mass of NTET can significantly affect the coupling frequency of the system. In the case of no spring prestress, larger mass, lower stiffness of the NTET can produce a better vibration suppression. But when the spring prestress is increased, the nonlinear stiffness of the NTET becomes weak, resulting in a reduction of control effect on the vortex-induced vibration. Parametric analysis shows that with the enhancement of vortex-induced vibration control effect, the vibration amplitude of cylinder can be decreased while the NTET’s amplitude is gradually increased, indicating the improvement of the energy transfer efficiency. The present research results can provide very useful theoretical support and experimental data for efficiently designing control strategies on vortex-induced vibrations in engineering fields.

2022, 54(11): 3147-3156. doi: 10.6052/0459-1879-22-293

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BURSTING OSCILLATIONS AND ENERGY HARVESTING EFFICIENCY ANALYSIS OF BISTABLE PIEZOELECTRIC ENERGY HARVESTER

Qian Youhua, Chen Yani

This paper theoretically analyzes the dynamic behavior of the bistable piezoelectric energy harvester by high-frequency excitation and the bursting oscillation by low-frequency excitation, in order to find multiple high-energy orbits for the system, so as to improve the energy harvesting efficiency. First, the structure and general model of the bistable piezoelectric energy harvester are introduced. Different from the research in engineering, this paper mainly studies the motion, voltage output and efficiency of the energy harvester in terms of dynamics, including the in-well low-energy-periodic motion and the inter-well chaos motion by high-frequency excitation. It is shown that the bistable piezoelectric energy harvester will produce bursting oscillation in inter-well high-energy orbits by a single low-frequency excitation, but only has periodic motion in in-well low-energy orbits. At the same time, the existence and intensity of the bursting oscillation are investigated in combination with the amplitude and well depth. To explain the effects of high- energy and low-energy orbits on the energy harvesting efficiency, the variation of the output voltage for different values of equivalent damping and load resistance is discussed, and the optimal matching is derived. Finally, in the case of multiple low-frequency external excitations, different orbital combination modes are analyzed. It is found that the output voltage of double-high-energy bursting oscillation mode is the largest, followed by the combination mode of single-high-energy bursting oscillation and single-low-energy periodic oscillation, and the output voltage of double-low-energy periodic oscillation mode is the lowest. The comparison with single external excitation shows the good performance of multiple excitations.

2022, 54(11): 3157-3168. doi: 10.6052/0459-1879-22-298

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VIBRATIONAL CHARACTERISTICS OF HONEYCOMB SANDWICH CANTILEVER PLATE WITH CURVED-WALL CORE

Xue Xiao, Zhang Junhua, Sun Ying, Quan Tiehan

As a kind of porous material, the honeycomb structure has the advantages of light weight, high strength, high stiffness, sound insulation, noise reduction, heat insulation and other excellent performance. Therefore, it is widely used in the field of transportation vehicles and aerospace etc. The traditional straight wall honeycomb is prone to stress concentration after loading, which will lead to crack failure and shorten the service life of the honeycombs. In order to solve this problem of honeycombs with straight walls, a honeycomb sandwich plate with circular arc core layer is designed in this paper. The equivalent parameters of honeycomb core are derived based on unit load method and the dynamic model of the curved-wall-core honeycomb sandwich plate is derived. The Chebyshev-Ritz method was used to solve the natural frequencies of honeycomb sandwich plate under cantilever boundaries, and the finite element method is used to compare. The errors of the first five natural frequencies are all within 5% from the two methods. The modes corresponding to each order of natural frequencies obtained from the finite element model are consistent with those obtained from the theoretical model. The curved honeycomb sandwich plate is prepared by 3D printing polylactic acid (PLA). The Young’s modulus of the printed PLA was measured by quasi-static tensile of the tensile specimen using a universal testing machine. The vibration test platform is built to do the sine sweep test, fixed frequency harmonic resides test and impact test. The comparison shows that the first five natural frequencies obtained from the vibration test of the 3D printing model verify the calculation results of the theoretical model and the finite element model. It is found that the curved-wall honeycomb core has a certain impact resistant performance in a specific frequency band. The obtained research results will provide theoretical support for the application of curved wall honeycombs in vibration and vibrational isolation.

2022, 54(11): 3169-3180. doi: 10.6052/0459-1879-22-305

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A FAST CALCULATION FOR THE SYMMETRY BREAKING POINT OF QUASI-PERIODIC RESPONSES

Gong Bingqing, Zheng Zechang, Chen Yanmao, Liu Jike

It has been a tough task to determine the bifurcation points of steady state responses such as periodic as well as quasi-periodic solutions arising in nonlinear dynamical systems. The calculation techniques and analysis methods have been well developed for periodic responses. Compared to periodic solutions, however, the solution techniques for quasi-periodic responses have only made relative progress in recent years, and the bifurcation analysis methods are even in more urgent need. To the best of our knowledge, for example, the bifurcation values of quasi-periodic responses have so far been usually determined by numerical approaches with the help of trail and error repeated calculation. For this issue, a fast calculation approach will be proposed in this paper, based on the incremental harmonic balance (IHB) method, to determine the bifurcation point for symmetry breaking of QP responses. The method is based on the fact that, the QP response can be described by generalized Fourier series with two irreducible frequencies. As the symmetry breaking happens, the coefficients of even-order (including the zeroth-order) harmonics will change from zero to non-zero small quantities. Based on this feature, the coefficient of the zeroth-order harmonic is priorly given as a small quantity. And the controlling parameter is incorporated as a variable into the IHB iteration scheme. The bifurcation point can be approximately determined as long as the iteration scheme is convergent. As illustrative examples, the Duffing oscillator and the Duffing-van der Pol coupled system, both subjected to multiple harmonic excitations with irreducible frequencies, are investigated by the proposed method. The symmetry breaking point can be efficiently determined, without any trail and error repeated calculation, as the convergent result can directly provide the controlling parameter close to the bifurcation value. In addition, it is shown that the calculation accuracy can be significantly improved by enhancing the number of truncated harmonics in the solution expression.

2022, 54(11): 3181-3188. doi: 10.6052/0459-1879-22-324

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INVERSE OF KEY PARAMETERS OF NONLINEAR FRICTION MODEL OF ROBOT JOINTS

Duan Shuyong, Duan Haodong, Han Xu, Li Changluo, Ouyang Heng, Li Yule, Liu Guirong

An accurate description of nonlinear friction of robot joints has important theoretical and scientific significance for improving trajectory accuracy, positioning accuracy and reliability of robot. However, the robot joints usually contain the motors, reducers, actuators and sensors, which are complex electromechanical coupling system. With the change of service time and working conditions, the friction parameters of robot joints also have significant time-varying effect, which is difficult to accurately describe, resulting in the decrease of trajectory accuracy and great difficulty for robot precision maintenance in the later stage. Therefore, this paper quantitatively evaluates the influence of friction parameters on the output torque of the robot, and proposes an inverse method for nonlinear friction parameters of the robot joints considering time-varying effects. Firstly, a general nonlinear friction model of the robot joint is established. The robot joint constant speed tracking experiment was designed, and the data collected by the experiment were processed by the Kalman filter. Then the relationship between the joint velocity and the driving motor current was established, and the general nonlinear friction model of the joint was established. Secondly, the key parameters of nonlinear friction model are selected. The dynamics model of robot containing nonlinear friction was established. The joint torques were calculated based on the excitation trajectory, and the friction parameters with high sensitivity to joint torques were selected for sensitivity analysis. Thirdly, a data set corresponding to the joint output torque and friction parameters is established. The friction parameter value space was constructed based on the actual working conditions, and the optimal Latin hypercube method was used to sample the friction parameters, which were substituted into the robot dynamics model to calculate the corresponding torques, and the one-to-one data set corresponding to the joint output torques and friction parameters were obtained. Finally, the inverse problem neural network is established and trained, and the key parameters of the nonlinear friction model are reversed and verified. The results illustrate that the accurate description of nonlinear joint friction reduces the influence of friction moment mutation on the trajectory of the robot, and significantly improves the trajectory accuracy.

2022, 54(11): 3189-3202. doi: 10.6052/0459-1879-22-252

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HIGH ORDER WEIGHT COMPACR NONLINEAR SCHEME FOR TIME-DEPENDENT HAMILTON-JACOBI EQUATIONS

Hu Yinggang, Jiang Yanqun, Huang Xiaoqian

Hamilton-Jacobi (HJ) equations are an important class of nonlinear partial differential equations. They are often used in various applications, such as physics, fluid mechanics, image processing, differential geometry, financial mathematics, optimal control theory, and so on. Because the weak solutions of the HJ equations exist but are not unique, and the spatial derivatives of the solutions may be discontinuous, numerical difficulties arise in numerical solutions of these equations. This paper presents a seventh-order weighted compact nonlinear scheme (WCNS) for the time-dependent HJ equations. This scheme is composed of the monotone Lax-Friedrichs flux splitting method for the Hamilton functions and the high-order hybrid cell-node and cell-edge central differencing for the left and right limits of first-order spatial derivatives in the numerical Hamilton functions. A high-order linear approximation scheme and four low-order linear approximation schemes for the unknowns at half nodes are derived based on a seven-point global stencil and four four-point sub-stencils, respectively. The smoothness indicators of the global stencil and four sub-stencils are also derived. In order to avoid non-physical oscillations of numerical solutions near the discontinuities and improve the numerical stability of the designed scheme, the WENO-type nonlinear interpolation technique is adopted to compute the unknowns at half nodes. The third-order TVD Runge-Kutta method is used for time discretization. The presented WCNS scheme is verified to have the optimal seventh order of accuracy for smooth solutions by theoretical analysis. For the sake of comparison, the classical seventh-order WENO scheme for solving hyperbolic conservation laws is also extended to solve the HJ equations. Numerical results show that the presented WCNS scheme can well simulate the exact solutions and can achieve seventh-order accuracy in smooth regions. Compared with the classical WENO scheme of the same order, the presented WCNS scheme has better accuracy, convergence and resolution, and its computational efficiency is slightly higher.

2022, 54(11): 3203-3214. doi: 10.6052/0459-1879-22-233

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TIME-DEPENDENT MECHANICAL BEHAVIOR AND CONSTITUTIVE PARAMETER IDENTIFICATION OF CHONDROCYTES BASED ON MACHINE LEARNING

Wei Xinyu, Sang Jianbing, Zhang Ruilin, Wang Jingyuan, Liu Baoyou

Research on the mechanical properties of chondrocytes under mechanical loading is crucial to understanding their normal and pathological states of chondrocytes and the etiology of osteoarthritis. Based on the highly complex nonlinear relationship between mechanical response and the constitutive parameters of the finite element method computational model of chondrocyte, two inversion methods were proposed to identify the MSnHS constitutive parameters of chondrocytes using the two-way deepnets (TW-Deepnets) model and random forest (RF) model, respectively, combined with the finite element method. Firstly, a three-dimensional finite element model was developed to simulate a stress relaxation unconfined compression test of a single cell. The spatial points of MSnHS constitutive parameters and corresponding finite element compression reaction force-response data were collected. Secondly, the TW-Deepnets model and RF model for chondrocyte parameter inversion were built by combining the Bayes hyperparameter optimization algorithm, and the data collected by the finite element method were trained by the machine learning models. Based on the experimental data of a single chondrocyte subjected to 50% compression, the MSnHS constitutive parameters of chondrocytes were reversed. Finally, the effectiveness of the proposed inversion methods were verified by comparison with the experimental curves from Nguyen, and the accuracy of the two methods was compared and evaluated by determinant coefficient R². The proportion of the importance of each parameter in the MSnHS constitutive model to the mechanical response of chondrocytes was analyzed, and the prediction performance of the two models for each constitutive parameter were tested. The results show that TW-Deepnets model and RF model combined with finite element method are effective and accurate method to identify the MSnHS constitutive material parameters of chondrocytes, and the obtained constitutive parameters can describe the time-dependent mechanical properties of chondrocytes. This method can also be extended to the complex parameters inversion problem of biological cells under static or dynamic loading conditions.

2022, 54(11): 3215-3222. doi: 10.6052/0459-1879-22-344

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ANALYSIS OF PERFORMANCE OF AMMONIA AIR-BREATHING VARIABLE CYCLE ENGINE

Zhang Xin, Lu Yang, Cheng Di, Fan Xuejun

In response to the demand of air-breathing power for wide-range aircraft with flight Mach number 0 ~ 10, a wide-range air-breathing variable cycle engine using ammonia as the fuel and coolant is proposed in the research. There are three working modes: turbine mode, pre-cooling mode and ramjet mode. Firstly, the feasibility of the engine at Mach 0 ~ 10 was preliminarily verified by modeling the thermodynamic cycle process of each mode and calculating the performance parameters such as specific thrust, specific impulse and total efficiency. Then, methane and decane were selected as the typical representatives of low temperature and low density and kerosene hydrocarbon fuels, and the performance of the engines fueled by ammonia and hydrocarbon fuels in turbine mode, pre-cooling mode and ramjet mode were comprehensively compared. The results show that due to the outstanding equivalent total heat sink and equivalent heat value of ammonia, the performance of it in the pre-cooling mode at Mach 3 ~ 5 is better than that of hydrocarbon fuels. In turbine mode and ramjet mode, the specific impulse of the engine using ammonia as the fuel is lower, but the specific thrust and total efficiency are better than that of hydrocarbon fuels. In the end, the operating characteristics of various fuels at Mach 0 ~ 10 were compared and analyzed, it shows that ammonia precooling can significantly improve engine performance in terms of wide-range operating characteristics, especially in the high Mach number, when ammonia is thermally decomposed into hydrogen and nitrogen in the regenerative cooling channel on the combustion chamber wall, the specific thrust and specific impulse of the engine will be further improved. And using ammonia as the coolant will not block the cooling channel, so it can meet the wide-range flight requirements of Mach 0 ~ 10. Kerosene hydrocarbon fuel is limited by low specific thrust and pyrolysis coking problems, and generally the maximum working Mach number does not exceed 8. In conclusion, the air-breathing variable cycle engine using ammonia as the fuel proposed in this paper has excellent equivalent cooling capacity and specific thrust index, and is suitable for applications such as the primary power of the two-stage orbiting vehicle, high Mach number air-breathing flight and future hypersonic civil aviation.

2022, 54(11): 3223-3237. doi: 10.6052/0459-1879-22-295

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