力学学报

CONSTITUTIVE MODELS AND HYPERGRAVITY PHYSICAL SIMULATION OF SOILS

Chen Yunmin, Ma Pengcheng, Tang Yao

Numerical simulation and physical simulation are two main methods to analyze the settlement and stability of soil mass. As the mathematical equations of the soil stress-strain relationships, constitutive models are the foundations of numerical simulation. Soil is a type of granular materials, leading to three essential characteristics of it including compressive hardening, shear dilatancy and friction. They are the main characteristics differing soils from metals and should be considered in constitutive model of soils. Traditional soil mechanics, which are widely applied in engineering at present, analyze the deformation and strength of soils separately by elastic theory and limit equilibrium theory based on rigid plasticity, respectively. However, the accuracy of their calculation results is generally difficult to satisfy the requirement of quantitative analysis because the essential characteristics of soils cannot be fully reflected. Cam-clay model is the first elasto-plastic constitutive model that can fully reflect the essential characteristics of soils. It unifies the deformation and strength of soils and can well describe the stress-strain relationships of normal consolidated clays; thus, Cam-clay model is regarded as the beginning of modern soil mechanics. Through introducing a unique unified hardening parameter, unified hardening model further develops the Cam-clay model and enlarges the application scope to over-consolidated clays. The authors believe that the challenge of constitutive model research in the future is how to consider the phase change of soil skeleton and the multi-field coupling in soils, to solve significant geotechnical problems in the field of energy, traffic, environment and hydraulic engineering, which cannot be analyzed quantitatively by current models. Due to the effects of scale compression and time compression, hypergravity physical simulation can overcome the disadvantage that stress level in small-scale model is lower than the prototype level in normal gravity physical simulation. Especially, hypergravity physical simulation is very appropriate to the problems of large scale and long duration. Compared with numerical simulation, hypergravity physical simulation has the advantages of being able to test the rationality of soil constitutive models and reveal the unknown features that cannot be described by current models. Finally, an engineering case of large-diameter steel pipe pile analyzed by combining numerical simulation and hypergravity physical simulation was presented.

2020, 52(4): 901-915. doi: 10.6052/0459-1879-20-059

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2020, 52(4): 916-916. doi: 10.6052/0459-1879-20-227

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REVIEW OF DYNAMIC MODELING AND STABILITY ANALYSIS OF A BICYCLE

Wang Nannan, Xiong Jiaming, Liu Caishan

The bicycle was invented more than two centuries ago. This seemingly ancient vehicle not only provides convenient transportation for people, but also attracts the interest of scholars from mathematics, physics, mechanics and other disciplines due to its unique motion characteristics and dynamic properties. Generally, a bicycle can be described as a rigid multi-body system with seven degrees of freedom, subjected to four nonholonomic constraints. However, due to the complex kinematic coupling between the front and rear wheels of a bicycle, its constraint equations and dynamic model become extremely complicated, leading to some vague knowledge about bicycle self-stability. Aiming at the classic Carvallo-Whipple bike configuration, this paper systematically reviewed the relevant problems in the research of bicycle dynamics in history. These problems include: (1) Mathematical description of geometric constraints and nonholonomic constraints for a bicycle moving on a complex curved surface; (2) The intrinsic symmetries of the bicycle system and the relevant conservation quantities; (3) Various modeling methods of bicycle dynamics; (4) The stability analysis of the relative equilibriums for the bicycle motions in a uniform linear motion on a horizontal surface and in a uniform circular motion on a surface of revolution, respectively; (5) Structural parameters affecting the bicycle self-stability, and etc. Finally, some typical experiments work and the different control strategies of the bicycle are detailedly described, and also several open problems are addressed for future research.

2020, 52(4): 917-927. doi: 10.6052/0459-1879-20-077

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DYNAMICAL CONTROL OF STABILITY FOR BIRKHOFFIAN SYSTEM

Chen Ju, Guo Yongxin, Liu Shixing, Mei Fengxiang

A dynamical control of the stability of equilibrium for the Birkhoffian system and generalized Birkhoffian system are studied. First, the equilibrium of motion and the equations of equilibrium of the systems are established. Secondly, the dynamical control of the stability of equilibrium for the Birkhoffian system where the Birkhoffian contain control parameters is investigated. The control parameters are chosen such that the Birkhoffian $B$ becomes a definite function and its derivative of time $\dot {B}$ is opposite sign. Thirdly, the dynamical control of the stability of equilibrium for Birkhoffian system where control parameters are contained in the Birkhoffian or in the additional terms is explored. Finally, some examples are given to illustrate the application of the results.

2020, 52(4): 928-931. doi: 10.6052/0459-1879-19-367

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NON-CONSERVATIVE NONLINEAR RIGID-ELASTIC-LIQUID- CONTROL COUPLING ANALYTICAL DYNAMICS AND ITS APPLICATIONS

Li Haibo, Liu Shixing, Song Haiyan, Liang Lifu

Non-conservative nonlinear rigid-elastic-liquid-control coupling analytical dynamics is one of the important research subjects related to aerospace dynamics and multi-body dynamics. It is of great theoretical significance and practical value to study this theoretical and applied subject by using analytical dynamics method. Firstly, the non-conservative nonlinear Hamilton-type quasi-variational principle of rigid-elastic-liquid-control coupling dynamics with two types of variables is established. Based on the functional of the Hamilton-type quasi-variational principle with two types of variables, the characteristics of rigid-elastic coupling, rigid-liquid coupling, elastic-liquid coupling and rigid-control coupling are analyzed. Secondly, with the help of Lagrange-Hamilton system, the Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is derived from Hamilton-type quasi-variational principle. Thirdly, the governing equations of the non-conservative nonlinear rigid-elastic-liquid-control coupling system are derived by applying the Lagrange equations. Based on the governing equations, the mechanisms of rigid-elastic coupling, rigid-liquid coupling , elastic-liquid coupling and rigid-control coupling are analyzed. The application of Lagrange equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system is studied in two aspects. On the one hand, the finite element model is established by applying the Lagrange equations. Furthermore, the advantages of this kind of computing model are analyzed. On the other hand, the problems are analyzed by using the governing equations of non-conservative nonlinear rigid-elastic-liquid-control coupling system. It illustrates the complementary characteristics of the application of analytic analysis and discussion to the study of problems and the application of numerical and quantitative analysis methods to the study of problems. Finally, several related issues are discussed.

2020, 52(4): 932-944. doi: 10.6052/0459-1879-20-107

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DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE

Yao Wenli, Liu Yanping, Yang Liusong

The Gauss's principle gives the rules to identify the real motion from the possible motion by finding the extreme value of the function, which can make the dynamic problem of the multi-body system not need to solve the differential (algebra) equation, but adopt the optimization method of solving the minimum value, therefore, how to define the appropriate Gaussian constraint function is the prerequisite for the realization of dynamic optimization method. For the ideal system, the effect of constraints on the system can be reflected by the constraint equation and so the Gaussian constraint can be expressed as a function of the particle acceleration of the system, then the dynamic problem of the system can be described as the constrained optimization problem with the objective function as the Gaussian constraint function and the optimization variable as the particle acceleration. When the non-ideal factors such as dry friction need to be taken into account in the system, the partial interaction can not be covered by the defined constraint equation and needs to be described by additional physical laws. This sort of interaction destroys the extreme value characteristics of the original Gaussian restraint function of the system. Based on Gauss's principle of the variable classification, the extreme value principle of non-ideal system is derived and proved, whose objective function is expressed by ideal constraint forces. The Gauss's principle for non-ideal system in the existing literature is discussed and it is pointed out that it is an expression of the extreme value principle given when there is no obvious function correlation between the non-ideal constraint force and the ideal constraint force. But when they have obvious function relation (such as the linear relationship between the sliding friction force and the normal constraint force in the Coulomb friction law), this form will fail. And according to the extreme value principle given, the dynamic optimization model of contact problem for multi-body system considering friction is obtained. In the examples, the optimization model and the corresponding linear complementary model are analyzed, which is found that the two are necessary and sufficient conditions for each other under the condition of satisfying the uniqueness of rigid body sliding problem, thus, the reliability of the optimization model given is proved. And the dynamic simulation is carried out by the optimization calculation method. The simulation results show the feasibility and effectiveness of combining Gaussian principle with optimization algorithm.

2020, 52(4): 945-953. doi: 10.6052/0459-1879-20-073

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UNCONSTRAINED MODAL ANALYSIS OF DYNAMIC MODEL OF FLEXIBLE SPACECRAFT

Song Xinyu, Ge Xinsheng

The influence coefficient of flexible coupling in dynamic modeling of flexible spacecraft is an important mechanical concept in dynamic modeling, which reflects the elastic vibration effect of spacecraft attitude and orbit motion and flexible accessories. The equivalent relationship between the influence coefficients of the flexible coupling, i.e. the inertial completeness criterion, is an important basis for the reduction of the order and the mode truncation of the dynamic model of the flexible spacecraft. Taking the center rigid body spacecraft with flexible appendages as the research object, the constrained mode and unconstrained mode are used to describe the structural deformation of flexible appendages, and the dynamic model of flexible spacecraft is established by using Euler Lagrange equation. Based on the research results of Hughes, the unconstrained modal identity of flexible spacecraft and the inertial completeness criterion for dynamic model reduction are proved and applied. The relationship between the inertia of two dynamic models is discussed, and the inertial completeness criterion of unconstrained mode is derived by using the inertial completeness criterion of constrained mode. Finally, the numerical simulation of the flexible spacecraft model composed of the central rigid body with two side solar panels and one side solar panels is carried out to find out the unconstrained mode translational coupling coefficient of the flexible appendages. The change of the unconstrained mode eigenvalue and translational coupling coefficient with the rigid flexible mass ratio is analyzed, and the mass characteristic identity of the unconstrained mode inertial completeness criterion is used to test the model The flexible spacecraft model is tested.

2020, 52(4): 954-964. doi: 10.6052/0459-1879-20-072

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DYNAMICS MODELING, SIMULATION, AND CONTROL OF ROBOTS WITH FLEXIBLE JOINTS AND FLEXIBLE LINKS

Fang Wuyi, Guo Xian, Li Liang, Zhang Dingguo

The effects of flexible joints on the dynamic response and control of robot are studied in this paper. Firstly, the spatial robot model consisting of $n$ flexible joints and $n$ flexible links is built, and the dynamic equations of the robot system are derived via the Lagrangian's equations. The tensile deformation, bending deformation, torsional deformation, and nonlinear coupling deformation of the flexible link are considered. Furthermore, the effects of the flexible joint are also considered in order to provide an important theoretical basis for the research of the vibration suppression and control of robots. The flexible joint is simplified as a linear torsion spring with damping, and the mass effect of the flexible joint is also considered in the model. Secondly, the dynamic simulations of the spatial manipulators are done to explore the effects of the joint stiffness and damping on the dynamic response of the robot system. The results show that as the stiffness coefficient increases, the amplitude of dynamic response of the flexible robot decreases, and the vibration frequency of the system becomes larger. As the damping coefficient increases, the dynamic response of the flexible robot decreases, and the dynamic response decays faster. The vibration of the flexible robot can be suppressed by adjusting the values of the stiffness and damping of the flexible joint. Finally, in order to study the effects of the flexibility of the joint on the control system, the rigid-joint manipulator and flexible-joint manipulator are made to move under the same circular motion. Then the joint torques of the two system are obtained respectively by solving the inverse dynamics equations, and the influence of the flexibility of the joint on the dynamics control is studied. The results show that the actuating torques required in the flexible-joint system are reduced compared to that required in the rigid-joint system.

2020, 52(4): 965-974. doi: 10.6052/0459-1879-20-067

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BUFFER AND COMPLIANT DYNAMIC SURFACE CONTROL OF SPACE ROBOT CAPTURING SATELLITE BASED ON COMPLIANT MECHANISM

Ai Haiping, Chen Li

The buffer and compliant control for space robot to avoid joint damage during on-orbit capture non-cooperative satellite are studied. For the reason, a compliant mechanism is mounted between the joint motor and space manipulator, its functions are: first, the deformation of internal spring in compliant mechanism can absorb the impact torque of the captured satellite acting on the joint of the space robot; second, the joint impact torque can be limited to a safe range by reasonably designing the buffer and compliant control scheme. First of all, the dynamic models of the space robot system and the target satellite system before capture are derived by multi-body theory. After that, based on the law of conservation of momentum, the constraints of kinematics and the law of force transfer, the integrated dynamic model of the combined system is derived. At the same time, the impact effect and impact force are calculated. For the stabilization control of post-capture unstable combined system, a buffer and compliant control scheme based on dynamic surface is proposed. The proposed control scheme can not only effectively absorb the impact torque generated by the on-orbit capture process, but also timely open or close the joint motor when the impact torque is too large, which can avoid overload and damage of the joint motor. In addition, the dynamic surface control scheme is utilized to avoid calculation expansion caused by backstepping method and to reduce the calculation effectively. The stability of the system is proved by Lyapunov theorem, and numerical simulation verifies the effectiveness of the proposed buffer and compliant control method.

2020, 52(4): 975-984. doi: 10.6052/0459-1879-20-068

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RESEARCH ON VIBRATION CHARACTERISTICS OF THE MANIPULATOR END UNDER ACTIVE CONTROL OF ARM STIFFNESS

Zhang Yuling, Gu Yongxia, Zhao Jieliang, Yan Shaoze

The structural deformation and elastic vibration of the manipulator will be caused by the flexibility of the manipulator arm during the movement, which will reduce the positioning accuracy and motion stability of the manipulator end. It is of great significance to apply structural vibration control method to the vibration suppression of the manipulator. Based on the design idea of variable stiffness active control, an active control method of arm stiffness is proposed. The stiffness of the manipulator is actively changed by changing the axial force of the manipulator arm. The nonlinear deformation of the manipulator is described by the deformation coupling method, and then the variable stiffness dynamic model of the manipulator arm is established by using the assumption mode method and Lagrange equation. Further, numerical simulation is performed to solve the variable stiffness dynamic model of the manipulator arm. On this basis, a single degree of freedom experimental device based on the active control of arm stiffness method is designed, and the vibration characteristics of the manipulator end under different preloading forces are analyzed. Numerical simulation and experimental results show that the vibration amplitude of the manipulator end is suppressed with the increase of preloading force, which verifies the effectiveness of the active control of arm stiffness. The relationship between the vibration response of the manipulator end and the preloading force is established by using the response surface method. Then the preloading force is optimized by using the Subspace Trust-region algorithm based on Interior-reflective Newton Method, and the optimal preloading force is obtained. This study can provide a theoretical basis for the fine dynamic modeling and the vibration suppression of the manipulator, and provide a direction for the study of the rigidization of economical low-stiffness materials, so as to replace the currently used expensive high-stiffness materials with cheap low-stiffness materials.

2020, 52(4): 985-995. doi: 10.6052/0459-1879-20-075

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ROLL CHARACTERISTICS OF ALL-TERRAIN VEHICLE BASED ON CROSSING DOUBLE AIR CHAMBER PNEUMATICALLY INTERCONNECTED SUSPENSION

Wang Zhen, Zhu Hengjia, Chen Xiaoyu, Zhang Yunqing

For the all-terrain vehicle with extremely high incidence of rollover accidents, a cross-type double air chamber pneumatically interconnection suspension using a capsule air spring is designed. A crossing double air chamber gas coupling AMEsim model and an all-terrain vehicle dynamics ADAMS/Car model are established. By taking the change of elastic force of air spring in the former model as the input variable of the vehicle dynamics model, and the compressional displacement of air spring in the latter model as the input variable of the gas coupling model, a complete mechanical-pneumatically coupling multi-degree of freedom dynamic joint simulation model is established. The roll characteristics of an all-terrain vehicle equipped with a crossing double air chamber pneumatically interconnected suspension(PIS), a crossing double air chamber pneumatically unconnected suspension(UN-PIS), and a common helical spring suspension(HS) are compared with the simulation experimental conditions. The results show that if the PIS system closes the interconnection pipeline, the UN-PIS system will be formed, which causes the suspension stiffness to rise sharply in an instant and the ride performance to deteriorate in an instant. On the premise of guarantee consistent vertical stiffness, PIS can provide greater lateral stiffness than HS. The factors affecting the dynamic roll characteristics in the gas pipeline system are researched, including the pipe length, pipe diameter and the volume of additional air chamber. The research shows that the shorter the pipe length is, the more beneficial it is to improve the roll characteristics of all-terrain vehicles. And there is a critical pipe diameter, when the pipe diameter is less than or greater than this value, the roll characteristics will be slightly improved. And the smaller the volume of the additional air chamber, the greater the lateral stiffness. Which provides a theoretical basis for the design of PIS system.

2020, 52(4): 996-1006. doi: 10.6052/0459-1879-20-071

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STABILITY ANALYSIS OF REUSABLE LAUNCH VEHICLE LANDING STRUCTURE

Yuan Han, Wang Xiaojun, Zhang Hongjian, Shi Yuhong, Zhang Xi, Zhang Ling

Many countries carried out the research on vertical take-off and vertical landing reusable launch vehicle (RLV) in recent years. The touchdown stability of the RLV when landing vertically on the platform is a key issue for the RLV reuse. Since the structural scheme of the RLV has not been completed in the initial stage of design, and there are no detailed dynamic models for touchdown stability analysis, it is difficult to carry out the dynamic simulation of landing process, therefore the research on estimation method of landing stability is needed. Based on the generalized impact law, this paper analyzes the multiple impacts between the RLV and the landing platform in a two-dimensional landing mode, and the tangential restitution coefficients is given by Coulomb friction model at the impulse level. Firstly, the admissible domain of restitution coefficients in the general motion mode is given through the energetic constraint and unilateral constraints, and the admissible domain of restitution coefficients in two typical motion modes is given as well. Secondly, considering the role of buffer in the landing leg, the collision between the RLV and the platform is approximated as a completely inelastic collision, and accordingly the kinematic restitution coefficients is obtained. Therefore, combined with the kinematic analysis and energy method, a touchdown stability criterion is proposed, which discriminates whether an RLV will fall or not after impacts the platform. In the end, taking an RLV landing prototype as an example, the effects of some key parameters on touchdown stability are analyzed, including the touchdown velocity, the span of supporting leg and the friction coefficient between supporting leg and platform. The results show that the touchdown stability criterion proposed in this paper, is more accurate than the energy method, and the coupling relationship between touchdown velocity, angular velocity and friction coefficient can be considered.

2020, 52(4): 1007-1023. doi: 10.6052/0459-1879-20-069

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COORDINATED PATH PLANNING BY INTEGRATING IMPROVED RRT* AND QUARTIC SPLINE

Yu Min, Luo Jianjun, Wang Mingming, Gao Dengwei

In order to perform an OOS (on-orbit servicing) mission of capturing a space non-cooperative target by space robot, this paper proposes a hierarchical coordinated path planning method for the free-floating dual-arm space robot, in which we consider the robot's constraints both kinematic and dynamic at the same time. First of all, a feasible end-effectors' path is initially planned via a state-of-the-art sampling-based method, named RRT* algorithm, in the Cartesian space, in which the sampling space is separated for two arms for the sake of possible self-collision avoidances of the dual-arm system during the high level of the path planning stage. Secondly, quartic splines are employed to smooth the path planned by RRT* algorithm during the low level of the trajectory planning stage. By designing the first-order derivative, the second-order derivative as well as the third-order derivative of these quartic splines, continuous differential constraints of the robot's path are well guaranteed. More importantly, we should integrate the robot's dynamic constraints within the design of differential constraints, such as the initial velocity, the initial acceleration and the final velocity of the end-effectors. After that, a smooth trajectory considering certain boundary constraints is obtained, which is dynamically feasible for the robot execution. Finally, the time of the whole path execution is calculated by considering the maximum physical limitation of the end-effectors. The minimum upper limit of maximum velocity and maximum acceleration of planned path of the end-effectors over its physical limitation is the minimum execution time. The proposed path planning method could design a coordinated path satisfying certain waypoints constraints for the robot. Besides, the physical limitation of the robot is also considered for the planned path. Moreover, the proposed path planning method is successfully validated on a free-floating dual-arm space robot and simulation results demonstrate the effectiveness of the proposed path planning method.

2020, 52(4): 1024-1034. doi: 10.6052/0459-1879-20-074

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VELOCITY-ACCELERATION STRUCTURE FUNCTION IN TWO-DIMENSIONAL DECAYING TURBULENCE

Zhou Zeyou

Second order velocity-acceleration structure function (VASF) is related to energy or enstrophy scale-to-scale transfer both in two-dimensional (2D) and three-dimensional (3D) turbulence, whose sign indicates the transfer direction. In 3D turbulence, energy transfers to smaller scale which results in negative VASF. In 2D turbulence, energy transfers to larger scale and enstrophy transfers to smaller scale, so the VASF are supposed to be positive in both inverse energy cascade range and direct enstrophy cascade range. However, comparing the abundant VASF researches in 3D turbulence, the sign of VASF in 2D turbulence is still lack of identification in neither experiment nor simulation. In this work, we give a general derivation which points out that apart from the scale-transfer term, the inhomogeneous term will also affect the VASF in spatial inhomogeneous turbulence. A commonly-used spatial inhomogeneous turbulence is that the turbulence below the turbulence generating device (such as comb) in wind tunnel or water tunnel. As flowing downstream, the turbulence intensity will decay, which brings the spatial inhomogeneity. We built a 2D decaying setup based on vertical soap-film flow, and performed particle tracking to measure VASF and its two components. Results show that the scale-transfer term is positive, but the inhomogeneous term is negative and dominates the VASF. As a result, the VASF is negative and lose its significance to identify the enstrophy transfers direction. Thus in similarly decaying turbulence, such as wind tunnel, water tunnel, sink et al., we shouldn't ignore the inhomogeneous term anymore. Finally, we discuss the dispersion process and find the slower dispersion is owing to the negative VASF.

2020, 52(4): 1035-1044. doi: 10.6052/0459-1879-20-056

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ANALYSIS OF UNSTEADY CAVITATION FLOW OVER HYDROFOIL BASED ON DYNAMIC MODE DECOMPOSITION

Xie Qingmo, Chen Liang, Zhang Guiyong, Sun Tiezhi

Cavitation is a special flow phenomenon with strong unsteadiness that often occurs in propeller of ships and underwater vehicles. The occurrence of cavitation often affects the hydrodynamic performance and efficiency of propulsion systems. In order to study the unsteady cavitation flow field structure around hydrofoil, numerical prediction and flow field structure analysis of unsteady cavitation flow around two-dimensional hydrofoil are investigated by using Schnerr-Sauer cavitation model and SST $k$-$\omega $ turbulence model. The validity of the established numerical method is verified by comparing the numerical prediction of cavitation evolution and pressure data with experimental results. The velocity field of the cavitation flow field is analyzed by using Dynamic Mode Decomposition (DMD). The results show that the first-order mode is 0Hz, which represents the average flow field. The second-order mode is about the frequency of cavitation shedding, which reveals the cavities grow and shed periodically at the leading edge of the hydrofoil. The third-order mode has a corresponding frequency about 2 times of the second order mode, which reveals that the fusion behavior of two large-scale vortices behind the hydrofoil. The fourth-order mode has a corresponding frequency about 3 times of the second order mode, which characterizes the fusion behavior of some small-scale eddies in the flow field. Finally, the modal decomposition analysis of the cavitation flow field under different cavitation numbers was carried out. It was found that the vortex structure of the shedding cavities increased with the decrease of the cavitation number, and the second-order mode frequency decreases with decreasing cavitation number.

2020, 52(4): 1045-1054. doi: 10.6052/0459-1879-20-062

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GENERAL REYNOLDS ANALOGY RELATION ON BLUNT-NOSED BODIES

Chen Xingxing, Chen Hao, Fan Jingjing, Wen Yufen, Zhang Zheng, Ma Youlin

The classical Reynolds analogy relation fail on blunt-nosed bodies, as the distributions of skin frictions on curved wall surfaces differ from that on heat fluxes. With a theoretical research background on hypersonic Reynolds analogy relations, numerical simulations are presented in this paper to study the general Reynolds analogy relation on blunt-nosed bodies, as circular cylinder and power-law body, under different incoming flows. A linear relation of Reynolds analogy is obtained by theoretical analysis on the boundary layer along those surfaces. Also, numerical methods are applied to obtain solutions of N-S equations, from which skin frictions and heat fluxes and their analogy coefficients around cylinders and power-law bodies are calculated. The methods are validated by comparing the distribution of Reynolds analogy coefficients and the stagnation point heat transfer rate with former numerical and theoretical results. The convergence and grid independence are verified for the TVD method. The variation of Reynolds analogy relations are investigated in the range of $Re_\infty = 3.98\times 10^2 \sim 1.59\times 10^6$ and $M_\infty = 3\sim 12$. The present study shows that the general Reynolds analogy relation predicts the ratio between skin frictions and heat fluxes on regimes near the stagnations point for hypersonic flows. Downstream the stagnation point of circular cylinders (where $\theta > 60^\circ$), the Reynolds analogy relation deviates from the theoretical linear relationship in varying degrees with the growing of Reynolds number. Numerical results demonstrate that, comparing with the general Reynolds analogy relations on circular cylinders, Reynolds analogy coefficients are lower and fit linear distributions better for power-law bodies. Analyses indicate that modifications based on the shape of noses or the Reynolds number may improve the accuracy of theoretical predictions.

2020, 52(4): 1055-1062. doi: 10.6052/0459-1879-19-365

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NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

Yao Chengbao, Fu Meiyan, Han Feng, Yan Kai

Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.

2020, 52(4): 1063-1079. doi: 10.6052/0459-1879-20-054

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EFFECT OF INTERLAYER THICKNESS ON THE MODE I FRACTURE ENERGY RELEASE RATE OF SANDWICH STRUCTURE

Zhang Fanfan, Song Jingru, Ma Hansong, Liu Xiaoming, Wei Yueguang

As a load transfer and connection element, the sandwich structure is widely used in aerospace, material characterization, flexible electronics and other fields. Understanding its fracture behavior and characteristics can provide theoretical guidance for designing the load capacity of the sandwich structure connector. In this paper, based on the improved elastic foundation theoretical model, we proposed a new theoretical model to calculate the energy release rate of the sandwich structure. The theoretical model considered the effect of the interlayer thickness on the energy release rate of the mode I fracture energy of the sandwich structure. Results showed that the influence of the middle layer on the energy release rate of mode I fracture has two parts: the influence of the shear force of the middle layer and the effect of the middle layer on the increase of structural stiffness. When the dimensionless interlayer thickness takes the maximum value of 2, the energy release rate from the traditional model may have a deviation greater than 70%, compared with the finite element calculation; our model can greatly improve the accuracy, and the error can be reduced to 5%. Compared with the improved elastic foundation theory, which is only applicable to the case where the thickness of the middle layer is small, the theoretical model has a wider range of applications. In addition, by using the present model, two geometric parameters (intermediate layer thickness and initial crack length) and one material parameter (modulus ratio) were selected for the study. The sensitivity of shear effect to structural geometry and material parameters was discussed. Based on the constant load, the influence of geometric and material parameters on the energy release rate was discussed; and on the assumption that the fracture toughness of the structure remains unchanged, the influence law of geometric and material parameters on the critical load of the sandwich structure was obtained.

2020, 52(4): 1080-1094. doi: 10.6052/0459-1879-20-092

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STUDY ON NONLINEAR CONSTITUTIVE RELATIONSHIP AND FRACTURE BEHAVIOR OF STITCHED C/SiC COMPOSITES

Cao Mingyue, Zhang Qi, Wu Jianguo, Ge Jingran, Liang Jun

C/SiC composites have a series of advantages such as high specific strength, high specific modulus, excellent thermal stability, etc, being widely used in the aerospace field. Brittle fracture caused by crack propagation is one of its main failure forms. Therefore, the fracture performance analysis of the material has important guiding significance for the structural design and application of the material. Simple mechanical experiments and fracture experiments of stitched C/SiC composites are carried out, the mechanical response and fracture characteristics of the materials under different loads being studied in the paper. Based on simple mechanical experiments of stitched C/SiC composites, the macroscopic nonlinear damage constitutive equation is established, and the fracture behavior of stitched C/SiC composites with unilateral notched beam and double cantilever beam are simulated. The constitutive equation uses simple equations to describe the nonlinear stress-strain curve of the material under complex stress conditions, and considers the crack closure on the reverse loading process. Based on the commercial finite element software ABAQUS, the non-linear damage constitutive equations are realized by writing a UMAT subroutine. The validity of the established constitutive equation is verified by a single element. On this basis, the linear elastic damage constitutive model and the nonlinear damage constitutive model are used to simulate the fracture behavior of the stitched C/SiC composites with a single-side notched beam and a double cantilever beam, respectively. The force-displacement curves simulated by the nonlinear damage constitutive equation are more consistent with the test results, and the failure load predicted by the nonlinear damage constitutive are closer to the test failure load, which verifies the accuracy of the nonlinear damage constitutive equation established in this paper. The paper provides a reference for the study of the fracture behavior of C/SiC composites and provides a theoretical basis for the design and application of stitched C/SiC composites structures.

2020, 52(4): 1095-1105. doi: 10.6052/0459-1879-20-058

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STUDY ON A DYNAMICS MODEL OF TAPPING MODE AFM AND ENERGY DISSIPATION MECHANISM

Wei Zheng, Zheng Xiaoting, Liu Jing, Wei Ruihua

In the tapping mode, the AFM probe experiences a continuous energy dissipation process when the probe gradually approaches the sample from a far distance to an intermittent contact. Researches on the energy dissipation mechanism of this continuous process still exists sporadically in various literatures, and there are few systematic explanations and experimental verifications for the energy dissipation mechanism of each stage in the continuous process. In this paper, a new simplified model of the AFM probe-sample system under displacement excitation is proposed, and a calculation method for the equivalent damping of the one-dimensional vibration system is obtained. By this method, the viscous damping of the air when the probe is far away from the sample surface and the air squeeze film damping when the probe is close to the sample are calculated. Finally, the change of the environmental dissipation mechanism in the process from the probe away from the sample to the intermittent contact with the sample surface is analyzed, and the relationship curve between the theoretical quality factors of the AFM system and the working positions of the probe is obtained. Based on this, the micro-cantilever frequency sweep experiments with different probes in tapping mode are carried out. The frequency sweep curves are obtained through the experiments, thus obtaining the experimental relationship curve between the quality factors of the system and the working positions of the probe. The accuracy of the theoretical model is verified from the experiments. Through theoretical analysis and experimental verification of the AFM environmental dissipation mechanism in tapping mode, a further understanding of the dynamics characteristics of tapping mode AFM and its damping mechanism will be provided by this study. At the same time, it provides theoretical reference and experimental methods for the research of the energy dissipation mechanism in Micro-nano electromechanical system (MEMS/NEMS).

2020, 52(4): 1106-1119. doi: 10.6052/0459-1879-20-099

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DYNAMIC RESPONSE OF SATURATED POROUS ELASTIC FOUNDATION UNDER POROSITY ANISOTROPY

Xiong Chunbao, Hu Qianqian, Guo Ying

Natural soils usually exhibit some anisotropic characteristics due to different deposition conditions and stress states. This study investigated the effects of coupled thermo-hydro-mechanical dynamics on an anisotropy of porosity, fully saturated, and poroelastic half-space subgrade whose surface is subjected to either thermal load or mechanical load in the direction of increasing the depth of the foundation and the direction of the wave propagation. Based on the Lord-Shulman generalized thermoelastic theory and the basic assumption of anisotropy of porosity, the coupled thermo-hydro-mechanical dynamic model for the porosity anisotropy saturated porous elastic foundation is established. The general relationships among non-dimensional vertical displacement, excess pore water pressure, vertical stress, and temperature distribution deduce by using normal mode analysis and depict them graphically. Normal mode analysis is a method using weighted residuals to derive analytical solutions and can thus solve partial differential equations more quickly compared to other methods. When the anisotropic parameter of porosity equals one the dynamic model of this anisotropic foundation can be reduced to a foundation model consistent with the coupled thermo-hydro-mechanical dynamic model, thus verifying the accuracy of the foundation model. The effects of anisotropic parameters of porosity on different physical variables are analyzed emphatically. The results show that the different anisotropic porosity coefficient parameters has a certain influence on all physical variables. The anisotropic porosity has a significant effect on the non-dimensional excess pore water pressure and the vertical stress when the upper surface of the foundation under thermal load, while has obviously effect on the excess pore water and temperature under mechanical load. As a whole, whatever the load is on the surface of the foundation, the peak of the curve decreases gradually and the location of the peak moves closer to the surface in the direction of increasing along the foundation depth as the increase of anisotropy parameters.

2020, 52(4): 1120-1130. doi: 10.6052/0459-1879-20-091

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NONLINEAR DYNAMIC RESPONSE OF PRE-DEFORMED BLADE WITH VARIABLE ROTATIONAL SPEED UNDER 2:1 INTERNAL RESONANCE

Gu Wei, Zhang Bo, Ding Hu, Chen Liqun

In the engineering practice, the rotating speed of turbine blade is not a constant value during many application scenarios, for example, during the start-up, the speed varying and the outage of engines, the input and output power of the rotor are out of balance, usually along with the generation of torsional vibration and resulting in velocity pulse. At the same time, the pre-deformation of the blades, caused by some factors including service environment and the installation imperfection, is often inevitable. Nonlinear dynamic behavior of pre-deformed blade with the varying rotating speed is studied in this paper. Considering the rotating speed is consisted of a constant speed and small perturbation, the dynamic governing equation is obtained by Lagrange principle. The partial differential equation is transformed into ordinary differential equation by using assumed mode method. For the sake of generality, a set of dimensionless parameters are introduced. The method of multiple scales is exploited to solve the excitation system. The average equation is derived in the case of 2:1 internal resonance. After that the steady-state response of the system is obtained. The influences of rotating speed, temperature gradient and damping on the dynamic behavior of the blade are studied in detail. Meanwhile, we clarify the effects of cubic nonlinear terms on the steady state response of the blade in the case of the 2:1 internal resonance. The original dynamic equation is integrated numerically in forward and backward frequency sweep direction to observe the jump phenomenon, and to verify the analytical solution. The results show that the changes of parameters have different influences on the dynamic behavior of blade. In the case of the 2:1 internal resonance, the cubic nonlinear terms have little influence on the dynamic response of the system. The analytical solutions are in good agreement with the numerical solutions.

2020, 52(4): 1131-1142. doi: 10.6052/0459-1879-20-060

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ON THE NONHOLONOMIC CONSTRAINTS AND MOTION CONTROL OF WHEELED MOBILE STRUCTURES1)

Zhou Yusheng, Wen Xiangrong, Wang Zaihua

When a particle moves along a smooth curve, the condition of zero lateral velocity should be satisfied. In the same way, different wheeled structures are all restrained by such nonholonomic constraint when they move along smooth curves on a plane. In this paper, holonomic and nonholonomic constraint equations of various kinds of wheeled structures are clarified, combined with the holonomic constraint relationship between the rotation speed of wheels and their motion speed. Then, the corresponding dynamical equations are readily derived by means of the Euler-Lagrange equation of nonholonomic mechanical systems. In addition, the target trajectory curve is converted to a form of speed target based on such nonholonomic constraint, and the relative curvature of target trajectory curve is introduced to design an appropriate dynamical tracking target. Furthermore, the motion law of the wheeled mobile structure can be organically combined with the dynamical equation by adopting such dynamical tracking target, and the original motion task can be simplified into a common trajectory tracking control problem. Consequently, an appropriate robust controller is designed to track the relative curvature of target trajectory curve on the basis of dynamical tracking target, such that the wheeled mobile structure can precisely follow the target trajectory curve. Theoretical analysis and simulation results indicate that the dynamical tracking target method can essentially solve the problem that the initial speed error is large enough and the position error is continuously accumulated. Even if the forward speed error system is not stable, the actual motion trajectory can almost be coincide with the target trajectory curve.

2020, 52(4): 1143-1156. doi: 10.6052/0459-1879-19-257

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DYNAMIC MODELING AND ANALYSIS OF THE LOWER LIMB PROSTHESIS WITH FOUR-BAR LINKAGE PROSTHETIC KNEE

Lü Yang, Fang Hongbin, Xu Jian, Ma Jianmin, Wang Qining, Zhang Xiaoxu

The four-bar linkage prosthetic knee has attracted widespread attention in the study of lower limb prosthesis because it shows a better bionic feature and a higher locomotive safety than the uniaxial joint prosthetic knee. Based on a real four-bar linkage prosthetic knee, this paper mainly studies the strongly nonlinear effects, e.g. the foot-ground interaction force and the unilateral constraint force of knee joint, on the gait of the lower limb prosthesis. For this purpose, firstly, the Kelvin-Voigt contact model is adopted to represent the effect of foot-ground contact force and the unilateral constraint force of the knee joint. The Coulomb model is employed to describe the effect of foot-ground friction force. Then, the Lagrange equations of the first kind are applied to model the dynamics of the prosthesis. Based on this model, the measured hip joint motion of an able-bodied testee is used as the driven signal and the gait characteristics analysis is conducted numerically. The numerical results reveal that if the stiffness of the hydraulic cylinder, which supports the motion of the prosthetic knee joint, is small, the strongly nonlinear effects may lead to the remarkable subharmonic response, which further results in the so-called gait inconformity. Further research shows that the subharmonic response can be avoided by lifting the hip joint, which provides a new insight into the compensatory mechanism such as lifting the hip for the amputee walking from the view of mechanics. In order to evaluate the consistence of the gaits between the prosthesis and the able-bodied testee, this paper further defines the correlation coefficient and analyzes the effects of the hydraulic cylinder's stiffness and damping on this coefficient. The results show that the correlation coefficient of the gaits can be better than 0.9 with proper stiffness and damping design. This discovery provides a solid foundation for further optimization of the four-bar linkage prosthesis.

2020, 52(4): 1157-1173. doi: 10.6052/0459-1879-20-048

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MULTI-MODE OSCILLATIONS AND HAMILTON ENERGY FEEDBACK CONTROL OF A CLASS OF MEMRISTOR NEURON

An Xinlei, Zhang Li

According to Faraday's electromagnetic induction law, the electrophysiological environment in and out the cell will produce electromagnetic induction effects in the case of ions penetrating the cell membrane or in the case of being exposed to external electromagnetic radiation, which will affect the electrical activity behavior of neural systems. Based on this principle, this paper studies the mixed-mode oscillation discharge characteristics of the Hindmarsh-Rose(HR) neuron model (here we call it as magnetic flux HR neuron model) with the influence of electromagnetic induction, and designs a Hamilton energy feedback controller to manage the mode to different periodic cluster discharge states. First, through theoretic analysis, it is found that the stability of equilibrium point in the magnetic flux HR neuron model is changed by the occurrence of Hopf bifurcation in the magnetic flux HR neuron model and a limit cycle is generated. Besides, some discharge characteristics of the membrane voltage near the Hopf bifurcation point are also discussed in detail. Then, it is also displayed there are abundant bifurcation structures in the magnetic flux HR neuron model based on the two-parameter numerical simulations, which includes multi-period bifurcation, period-adding bifurcation with chaos, period-adding bifurcation without chaos and co-existing mixed-mode oscillations in different initial conditions. At last, with the purpose of controlling the mixed-mode oscillation of membrane voltage, the Hamilton energy function is calculated by utilizing the Helmholtz theorem, and a Hamilton energy feedback controller is designed further. Additionally, it can be seen that the controller can effectively control the membrane voltage in different periodic clustering discharge modes, with the analysis of the discharge states of membrane voltage under different feedback gains in view of the numerical simulation. The results of this paper provide a useful theoretical support for the study of bifurcation structure in artificial neuron system under electromagnetic induction and the field of energy control related to the neurons.

2020, 52(4): 1174-1188. doi: 10.6052/0459-1879-20-035

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NON-AXISYMMETRIC MIXED BOUNDARY VALUE PROBLEM FOR DYNAMIC INTERACTION BETWEEN SATURATED POROUS FOUNDATION AND RECTANGULAR PLATE

Wang Li'an, Zhao Jianchang, Yang Huazhong

Multiple boundary conditions exist in different areas of the same boundary surface are called mixed boundary, which is a well-known mechanical problem. It is necessary to solve the mixed boundary value problem, when to accurately analyze such problems. For the general 3D non-axisymmetric situation, there are often mathematical difficulties in solving the mixed boundary value problem. In this paper, an analytical method for solving three-dimensional non-axisymmetric mixed boundary value problems is presented by using Hilbert's theorem and double Fourier transform. Basted on this method, the coupled vibration problem for a rectangular plate resting on a saturated porous half-space with mixed permeable boundary is studied. Firstly, the dynamic governing equations of rectangular plates and saturated porous foundations are established based on Kirchhoff theory and Biot's porous medium theory. The operator equation is decoupled by double Fourier transforms to obtain the general solution of the rectangular plate and the foundation. The mixed boundary value problem is converted to two pairs of two-dimensional dual integral equations, with the contact surface stress and pore pressure as the basic unknowns, and to be solved by the Schmidt's method. The displacement and internal force analytical equations of the coupled vibration of the plate-foundation system are obtained. Finally, numerical examples are given to analyze and discuss the vibration response and parameters of the rectangular substrate on the saturated half space.

2020, 52(4): 1189-1198. doi: 10.6052/0459-1879-19-345

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RESEARCH ON ELECTROMAGNETIC RADIATION DURING THE EXPLOSION PROGRESS OF COMPOSITION B EXPLOSIVES

Ren Huilan, Chu Zhuxin, Li Jianqiao, Ma Tianbao

The electromagnetic radiation interference, which can be obviously observed during the explosives process, has attracted attention in many fields. However, the corresponding generation mechanism and theoretical model are still immature, experiments are still the key approach to study this phenomenon. This paper designs experiments to collect the electromagnetic radiation signals, generated by different charges of composition B explosives (Comp B), and uses the wavelet transform method to obtain these signals time-frequency characteristics, namely the main spectrum distribution is in the range of 0$\sim$50 kHz. Furthermore, the self-developed EXPOSION-3D software is used to simulate the experimental conditions to obtain the characteristics of the flow field during the explosion. By comparing the experimental results with the numerical simulations, series of conclusions are given in the following. The first pulse signal is the electromagnetic pulse directly generated by the high-temperature and high-pressure plasma generated by the detonation of Comp B; the second pulse signal is an electromagnetic pulse generated by the plasma formed at the air shock wave front which is caught up by the reflected shock wave from the ground; the third pulse signal is an invalid signal caused by the shock wave hitting the measurement coils. The amplitude of the first electromagnetic pulse has a linear relationship with the 1/3 power of the charge, and its arrival time is not sensitive to the charge of explosive. The time of the second electromagnetic pulse is in an exponential relationship with the charge of explosive. Overall, this paper put forward the characteristics of the explosion wave flow field when the shock wave reflection forms the electromagnetic wave signal, which provides verification data for the subsequent theoretical research.

2020, 52(4): 1199-1210. doi: 10.6052/0459-1879-20-010

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REVIEW OF THE THIRD NATIONAL SYMPOSIUM ON EXPLOSION AND IMPACT DYNAMICS FOR YOUNG SCHOLARS

Gao Guangfa, Lei Tiangang, Dai Lanhong

The Third National Symposium on Explosion and Impact Dynamics for Young Scholars was briefly introduced and all of the scientific reports presented at this symposium were reviewed. The scientific reports include four invited talks, nineteen thematic invitations and seventeen topic invitations, which were divided into five research topics, i.e. Detonation and Explosion Dynamics, Structural Dynamics and Multi-scale High Performance Computing, Material Dynamics and Experimental Testing Techniques, Dynamic Mechanical Behavior of Composite Structures, and Energy Absorption Characteristics and Optimization Design of Lightweight Structures. The symposium provides an excellent platform for the young scholars in the Explosion Mechanics and Impact Dynamics to conduct academic exchanges, establish academic friendship and enhance academic cooperation, and it also plays an active role in the construction and development of the discipline.

2020, 52(4): 1211-1219. doi: 10.6052/0459-1879-20-150

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