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1.  Numerical and experimental studies on impact dynamics of a planar flexible multibody system  
   Fu-Xiang Dong · Jia-Zhen Hong · Kun Zhu · Zheng-Yue Yu Department of Engineering Mechanics  Shanghai Jiaotong University   Shanghai  China《Acta Mechanica Sinica》,2010年第26卷第4期
   In this paper a computational methodology on impact dynamics of the flexible multibody system is presented. First, the floating frame of reference approach and nodal coordinates on the basis of finite element formulation are used to describe the kinematics of planar deformable bodies. According to the kinematic description of contact conditions, the contact constraint equations of planar flexible bodies are derived. Based on the varying topology technique the impact dynamic equations for a planar multibody system are established. Then the initial conditions of the equations in each contact stage are determined according to the discontinuity theory in continuum mechanics. The experiments between the aluminum rods are performed to check the correctness of the proposed method. Through the comparison between the numerical and experimental results the proposed method is validated. Experimental results also show that the impulse momentum method cannot accurately predict the complex impact dynamic phenomena and the continuous model may lead to a serious error when used to simulate the impact problems with significant wave propagation effects.    

2.  Contact-impact formulation for multi-body systems using component mode synthesis  
   Peng Chen  Jin-Yang Liu  Jia-Zhen Hong《Acta Mechanica Sinica》,2013年第29卷第3期
   The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts: a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom (DOFs) are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.    

3.  A new subregion mesh method for the investigation of the elastic-plastic impact in flexible multibody systems  
   Peng Chen  Jin-Yang Liu  Guang-Can Lu《Acta Mechanica Sinica》,2017年第33卷第1期
   Impact processes between flexible bodies often lead to local stress concentration and wave propagation of high frequency. Therefore, the modeling of flexible multi-body systems involving impact should consider the local plastic deformation and the strict requirements of the spa-tial discretization. Owing to the nonlinearity of the stiffness matrix, the reduction of the element number is extremely important. For the contact-impact problem, since different regions have different requirements regarding the element size, a new subregion mesh method is proposed to reduce the number of the unnecessary elements. A dynamic model for flexible multibody systems with elastic-plastic contact impact is established based on a floating frame of reference formulation and complete Lagrange incremental nonlin-ear finite-element method to investigate the effect of the elastic-plastic deformation as well as spatial discretization. Experiments on the impact between two bodies are carried out to validate the correctness of the elastic-plastic model. The proposed formulation is applied to a slider-crank system with elastic-plastic impact.    

4.  New method for oblique impact dynamics research of a flexible beam with large overall motion considering impact friction force  
   W. Yuan  L. Li  D. G. Zhang  J. Z. Hong《Acta Mechanica Sinica》,2016年第32卷第4期
   A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid mod-eling method, dynamic equations of the system, which include all states (before, during, and after the collision) are obtained. Simulation results of a concrete example are compared with the results obtained from two other models: a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.    

5.  Modeling and analysis of rigid multibody systems with driving constraints and frictional translation joints  
   Fang-Fang Zhuang  Qi Wang《Acta Mechanica Sinica》,2014年第30卷第3期
   An approach is proposed for modeling and anal- yses of rigid multibody systems with frictional translation joints and driving constraints. The geometric constraints of translational joints with small clearance are treated as bilat- eral constraints by neglecting the impact between sliders and guides. Firstly, the normal forces acting on sliders, the driv- ing constraint forces (or moments) and the constraint forces of smooth revolute joints are all described by complementary conditions. The frictional contacts are characterized by a set- valued force law of Coulomb's dry friction. Combined with the theory of the horizontal linear complementarity problem (HLCP), an event-driven scheme is used to detect the transi- tions of the contact situation between sliders and guides, and the stick-slip transitions of sliders, respectively. And then, all constraint forces in the system can be computed easily. Secondly, the dynamic equations of multibody systems are written at the acceleration-force level by the Lagrange multiplier technique, and the Baumgarte stabilization method is used to reduce the constraint drift. Finally, a numerical example is given to show some non-smooth dynamical behaviors of the studied system. The obtained results validate the feasibility of algorithm and the effect of constraint stabilization.    

6.  Wear analysis of revolute joints with clearance in multibody systems  
   BAI ZhengFeng  ZHAO Yang  WANG XingGui《中国科学:物理学 力学 天文学(英文版)》,2013年第8期
   In this work, the prediction of wear for revolute joint with clearance in multibody systems is investigated using a computational methodology. The contact model in clearance joint is established using a new hybrid nonlinear contact force model and the friction effect is considered by using a modified Coulomb friction model. The dynamics model of multibody system with clearance is established using dynamic segmentation modeling method and the computational process for wear analysis of clearance joint in multibody systems is presented. The main computational process for wear analysis of clearance joint includes two steps, which are dynamics analysis and wear analysis. The dynamics simulation of multibody system with revolute clearance joint is carried out and the contact forces are drawn and used to calculate the wear amount of revolute clearance joint based on the Archard’s wear model. Finally, a four-bar multibody mechanical system with revolute clearance joint is used as numerical example application to perform the simulation and show the dynamics responses and wear characteristics of multibody systems with revolute clearance joint. The main results of this work indicate that the contact between the joint elements is wider and more frequent in some specific regions and the wear phenomenon is not regular around the joint surface, which causes the clearance size increase non-regularly after clearance joint wear. This work presents an effective method to predict wear of revolute joint with clearance in multibody systems.    

7.  Stability analysis of liquid filled spacecraft system with flexible attachment by using the energy–Casimir method  
   《力学快报》,2016年第2期
   The stability of partly liquid filled spacecraft with flexible attachment was investigated in this paper.Liquid sloshing dynamics was simplified as the spring–mass model, and flexible attachment was modeled as the linear shearing beam. The dynamic equations and Hamiltonian of the coupled spacecraft system were given by analyzing the rigid body, liquid fuel, and flexible appendage. Nonlinear stability conditions of the coupled spacecraft system were derived by computing the variation of Casimir function which was added to the Hamiltonian. The stable region of the parameter space was given and validated by numerical computation. Related results suggest that the change of inertia matrix, the length of flexible attachment,spacecraft spinning rate, and filled ratio of liquid fuel tank have strong influence on the stability of the spacecraft system.    

8.  ANALYSIS ON TRANSVERSE IMPACT RESPONSE OF AN UNRESTRAINED TIMOSHENKO BEAM  被引次数:1
   陈镕  郑海涛  薛松涛  唐和生  王远功《应用数学和力学(英文版)》,2004年第25卷第11期
   A moving rigid-body and an unrestrained Timoshenko beam, which is subjected to the transverse impact of the rigid-body, are treated as a contact-impact system. The generalized Fourier-series method was used to derive the characteristic equation and the characteristic function of the system. The analytical solutions of the impact responses for the system were presented. The responses can be divided into two parts : elastic responses and rigid responses. The momentum sum of elastic responses of the contact-impact system is demonstrated to be zero, which makes the rigid responses of the system easy to evaluate according to the principle of momentum conservation.    

9.  Contact dynamics of elasto-plastic thin beams simulated via absolute nodal coordinate formulation  
   Qing-Tao?Wang  Qiang?Tian  Email author&prev_q=Hai-Yan?HuEmail author" target="_blank">Hai-Yan?HuEmail author《Acta Mechanica Sinica》,2016年第32卷第3期
   Under the frame of multibody dynamics, the contact dynamics of elasto-plastic spatial thin beams is numerically studied by using the spatial thin beam elements of absolute nodal coordinate formulation (ANCF). The inter-nal force of the elasto-plastic spatial thin beam element is derived under the assumption that the plastic strain of the beam element depends only on its longitudinal deformation. A new body-fixed local coordinate system is introduced into the spatial thin beam element of ANCF for efficient con-tact detection in the contact dynamics simulation. The linear isotropic hardening constitutive law is used to describe the elasto-plastic deformation of beam material, and the classical return mapping algorithm is adopted to evaluate the plastic strains. A multi-zone contact approach of thin beams previ-ously proposed by the authors is also introduced to detect the multiple contact zones of beams accurately, and the penalty method is used to compute the normal contact force of thin beams in contact. Four numerical examples are given to demonstrate the applicability and effectiveness of the pro-posed elasto-plastic spatial thin beam element of ANCF for flexible multibody system dynamics.    

10.  Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space  
   Edwin Kreuzer《Acta Mechanica Sinica》,2012年第28卷第2期
   In this paper,by defining new state vectors and developing new transfer matrices of various elements moving in space,the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space.Formulations and numerical example of a rigidflexible-body three pendulums system moving in space are given to validate the method.Using the new method to study the dynamics of multi-rigid-flexible-body system moving in space,the global dynamics equations of system are not needed,the orders of involved matrices of the system are very low and the computational speed is high,irrespective of the size of the system.The new method is simple,straightforward,practical,and provides a powerful tool for multi-rigid-flexible-body system dynamics.    

11.  IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX  
   赵振  陈滨  刘才山  金海《Acta Mechanica Sinica》,2004年第20卷第6期
   Painlevé‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.    

12.  Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method  被引次数:1
   Jing Zhao  Hai-Yan Hu  Qiang Tian《Acta Mechanica Sinica》,2013年第29卷第1期
   The spinning solar sail of large scale has been well developed in recent years. Such a solar sail can be considered as a rigid-flexible multibody system mainly composed of a spinning central rigid hub, a number of flexible thin tethers, sail membranes, and tip masses. A simplified interplanetary kite-craft accelerated by radiation of the Sun (IKAROS) model is established in this study by using the absolute-coordinate-based (ACB) method that combines the natural coordinate formulation (NCF) describing the central rigid hub and the absolute nodal coordinate formulation (ANCF) describing flexible parts. The initial configuration of the system in the second-stage deployment is determined through both dynamic and static analyses. The huge set of stiff equations of system dynamics is solved by using the generalized-alpha method, and thus the deployment dynamics of the system can be well understood.    

13.  PARALLEL DYNAMIC ITERATION METHODS FOR SOLVING NONLINEAR TIME—PERIODIC DIFFERENTIAL—ALGEBRAIC EQUATIONS  
   YaolinJiang《计算数学(英文版)》,2003年第21卷第3期
   In this paper we presented a convergence condition of paralle dynamic iteration meth-ods for a nonlinear system of differential-algebraic equations with a periodic constraint.The convergence criterion is decided by the spectral expressjon of a linear operator derived form system partitions.Numerical experiments given here confirm the theoretical work of the paper.    

14.  Coupling dynamic analysis of spacecraft with multiple cylindrical tanks and flexible appendages  
   Wen-Jun Wu  Bao-Zeng Yue  Hua Huang《Acta Mechanica Sinica》,2016年第32卷第1期
   This paper is mainly concerned with the coupling dynamic analysis of a complex spacecraft consisting of one main rigid platform, multiple liquid-filled cylindrical tanks,and a number of flexible appendages. Firstly, the carrier potential function equations of liquid in the tanks are deduced according to the wall boundary conditions. Through employing the Fourier–Bessel series expansion method, the dynamic boundaries conditions on a curved free-surface under a low-gravity environment are transformed to general simple differential equations and the rigid-liquid coupled sloshing dynamic state equations of liquid in tanks are obtained. The state vectors of rigid-liquid coupled equations are composed with the modal coordinates of the relative potential function and the modal coordinates of wave height. Based on the Bernoulli–Euler beam theory and the D'Alembert's principle, the rigid-flexible coupled dynamic state equations of flexible appendages are directly derived, and the coordinate transform matrixes of maneuvering flexible appendages are precisely computed as time-varying. Then, the coupling dynamics state equations of the overall system of the spacecraft are modularly built by means of the Lagrange's equations in terms of quasi-coordinates. Lastly, the cou-pling dynamic performances of a typical complex spacecraft are studied. The availability and reliability of the presented method are also confirmed.    

15.  Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops  
   李群宏  谭洁燕《中国物理 B》,2011年第20卷第4期
   A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process,the Poincar′e map of the system is constructed. Using the Poincar′e map and the Gram-Schmidt orthonormalization,a method of calculating the spectrum of Lyapunov exposents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method,the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.    

16.  Simulation of ball motion and energy transfer in a planetary ball mill  被引次数:1
   陆胜勇  毛琼晶  彭政  李晓东  严建华《中国物理 B》,2012年第21卷第7期
   A kinetic model is proposed for simulating the trajectory of a single milling ball in a planetary ball mill, and a model is also proposed for simulating the local energy transfer during the ball milling process under no-slip conditions. Based on the kinematics of ball motion, the collision frequency and power are described, and the normal impact forces and effective power are derived from analyses of collision geometry. The Hertzian impact theory is applied to formulate these models after having established some relationships among the geometric, dynamic, and thermophysical parameters. Simulation is carried out based on two models, and the effects of the rotation velocity of the planetary disk and the vial-to-disk speed ratio ω/Ω on other kinetic parameters is investigated. As a result, the optimal ratio ω/Ω to obtain high impact energy in the standard operating condition at = 800 rpm is estimated, and is equal to 1.15.    

17.  CONSTRAINT VIOLATION STABILIZATION OF EULER-LAGRANGE EQUATIONS WITH NON-HOLONOMIC CONSTRAINTS  
   ZhaoWeijia PanZhenkuan ChenLiqun《Acta Mechanica Solida Sinica》,2004年第17卷第1期
   Two constraint violation stabilization methods are presented to solve the Euler Lagrange equations of motion of a multibody system with nonholonomic constraints. Compared to the previous works, the newly devised methods can deal with more complicated problems such as those with nonholonomic constraints or redundant constraints, and save the computation time. Finally a numerical simulation of a multibody system is conducted by using the methods given in this paper.    

18.  Dynamic analysis of an offshore pipe laying operation using the reel method  
   Marek Szczotka《Acta Mechanica Sinica》,2011年第27卷第1期
   A system designed for a rigid and flexible pipe laying purposes is presented in the paper.Mathematical and numerical models are developed by using the rigid finite element method(RFEM).The RFEM is an efficient solution in the time domain.Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method.Large deformations of the pipe during spooling and when it is reeled out at sea are considered.A material model implemented is used to take into consideration nonlinear material properties.In particular,the full elasto-plastic material characteristics with hardening and Bauschinger effect are included.Dynamic analyses are performed and the results attached in this work demonstrates how the sea conditions influence the machinery and pipeline,assuming a passive reel drive system. The influence of several other operational parameters on dynamic loads is verified.An active system,implemented as a part of the mathematical model,improves the system performance.Some results are presented as well.    

19.  A BOUNDARY-ELEMENT METHODFOR NONLINEARSLAMMING  
       叶天麒《固体力学学报》,1999年第20卷第2期
   Thenonlinear condition of water-surface is considered,and by virtue of the boundary elementmethod,the slamming problem is treated as an impact/contact model,where the impactorand water are regarded as a coupling system.The gradually iterative method is used tomake that water-surface satisfies the nonlinear condition untill it achives a steady value.Forsolving of the slamming force,the gradually iterative approach connected with the freewater-surface is used to calculate the steady value.Two-dimensional rigid cylinderslamming problems are analysed numerically.The results show the reliability andeffectiveness for solving the fluid-structure impact problems with serious nonlinearities.    

20.  Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper  
   Ying-Hong Jia  Shi-Jie Xu  Quan Hu《Acta Mechanica Sinica》,2013年第29卷第2期
   This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane’s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.    

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