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Bicycle dynamics and its circular solution on a revolution surface

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Acta Mechanica Sinica 2020年第1期36卷 220-233页

作者： Jiaming Xiong Nannan Wang caishan liu State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking UniversityBeijing100871China

In this paper,we study the dynamics of an idealized benchmark bicycle moving on a surface of *** employ symbolic manipulations to derive the contact constraint equations from an ordered process,and apply the Lagrangian equations of the first type to establish the nonlinear differential algebraic equations(DAEs),leaving nine coupled differential equations,six contact equations,two holonomic constraint equations and four nonholonomic constraint *** then present a complete description of hands-free circular motions,in which the time-dependent variables are eliminated through a rotation *** find that the circular motions,similar to those of the bicycle moving on a horizontal surface,nominally fall into four solution families,characterized by four curves varying with the angular speed of the front ***,we numerically investigate how the topological profiles of these curves change with the parameter of the revolution ***,we directly linearize the nonlinear DAEs,from which a reduced linearized system is obtained by removing the dependent coordinates and counting the symmetries arising from cyclic *** stability of the circular motion is then analyzed according to the eigenvalues of the Jacobian matrix of the reduced linearized system around the equilibrium *** find that a stable circular motion exists only if the curvature of the revolution surface is very small and it is limited in small sections of solution ***,based on the numerical simulation of the original nonlinear DAEs system,we show that the stable circular motion is not asymptotically stable.

关键词： Bicycle dynamics Nonholonomic constraints Stability Nonlinear DAEs Circular motion

The compliance contact model of cylindrical joints with clearances

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Acta Mechanica Sinica 2005年第5期21卷 451-458页

作者： caishan liu Ke Zhang Lei Yang Department of Mechanics and Engineering Science State Key Laboratory of Turbulence and Complex SystemsPeking University Beijing 100871 China Chinese Academe of Space Technology Beijing 100086 China

This paper is concerned with the determination of the normal force-displacement （NFD） relation for the contact problem of cylindrical joints with clearance. A simple formulation for this contact problem is developed by modeling the pin as a rigid wedge and the elastic plate as a simple Winkler elastic foundation. The numerical results show that the normal displacement relation based on Hertz theory is only valid for the case of large clearance with a small normal load, and the NFD relation based on Persson theory is only effective in the case of very small clearance. The proposed approximate model in this paper gives better results than Hertz theory and Persson theory in a large range of clearances as seen from the comparison with the results of FEM.

关键词： Cylindrical joint with clearance .Conformalcontact. FEM

Continuum description for the characteristic resistance sensed by a cylinder colliding against granular medium

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Science China(Physics,Mechanics & Astronomy) 2013年第8期56卷 1428-1436页

作者： PANG Yong liu caishan State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking University

In this paper, we experimentally and theoretically study the resistance force that develops when a cylinder with a flat face colliding against dry quartzite sand. Observations from experimental data clearly show that the acceleration curves are characterized by a double-peak structure. The first agitated peak can be attributed to a shock process where sand responds elastically, and the valley bottom in the double-peak structure is related to a limited plastic load when a fully plastic region is formed in the sand, while the second agitated peak corresponds to a the occurrence of the maximum of viscous force in a homogeneous developed bulk flow. We use slip line theory (SL) developed in plastic mechanics to capture the value at the valley bottom, adopt the double shearing theory (DS), together with a Local Rheological Constitutive Law (LRCL) suggested in this paper, to capture the drag force generated in a homogeneous bulk flow. Good agreements in the comparisons between numerical and experimental results support the characteristic resistance by the cylinder to predict granular states.

关键词： granular material penetrating dynamics rheological property

2D numerical model for studying frictional sliding

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Acta Mechanica Sinica 2020年第3期36卷 742-753页

作者： Xisheng Li Zhihua Zhao Jiaming Xiong caishan liu State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking UniversityBeijing 100871China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China

The onset of frictional motion couples complex spatiotemporal dynamics of discrete contacts with different orders of magnitude at time and length *** order to reveal how these individual scales affect the frictional sliding,we establish a 2D multiscale spring-block model for the frictional sliding at an elastic slider-rigid *** this model,the rupture of frictional interface is described by three different types of locally microscopic motion:pinned,sliding and dislocated *** using realistic boundary conditions,our numerical results can precisely reproduce the loading curves found in previous *** precursor events,corresponding to a discrete sequence of rapid crack-like fronts propagating partially in the contact zone,can also be shown in our *** the analysis of the microscopic motion,we characterize the evolution of the real contact area and the corresponding interface motion at the mesoscale level,and show that the evolution corresponds to four distinct and inter-related phases:detachment,fast and slow slip motion,as well as the rest of *** mesoscale behaviors are completely consistent with the existing experimental results and their physical mechanisms can be explained by the detailed information of the numerical *** study is established on a bottom-up multiscale model which provides a comprehensive picture about the complex spatiotemporal dynamics of frictional sliding.

关键词： Friction Multiscale model Simulation

Nonlinear wave in granular systems based on elastoplastic dashpot model

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International Journal of Mechanical System Dynamics 2021年第1期1卷 132-142页

作者： Gengxiang Wang caishan liu State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking UniversityBeijingChina

The dynamic dashpot models are widely used in EDEM commercial ***,most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact ***,the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact *** two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular ***,this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular ***,the entire contact process is divided into three different phases:elastic,elastoplastic,and full plastic *** Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic *** contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma‐liu(ML)model in each time ***,the whole contact behavior is treated as a linear mass‐spring‐damper model,and the damping factor is obtained by solving the single‐degree‐freedom underdamped vibration *** new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors,which not only removes the initial im-pact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic ***,a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental *** simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.

关键词： dynamic dashpot model granular chain numerical singularity solitary wave

Study on the static properties of spiral springs under static loading

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Applied Mathematics and Mechanics(English Edition) 2021年第11期42卷 1571-1580页

作者： Zhixiang LI Zhen ZHAO caishan liu Qingyun WANG School of Aeronautic Science and Engineering Beihang UniversityBeijing 100191China State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking UniversityBeijing 100871China

Spiral springs have a wide range of applications in various *** a result of the complexity of friction,few theoretical analyses of spring belts under static loading have been carried *** the piecewise smooth property of the whole contact area,a simplified static model of spiral springs under loading is established in this ***,three main stress and friction distribution areas of the spring belt are proposed,namely,internal,transitional,and external *** the outermost side of the spring is not subject to any pressure,a recursive method is adopted from the outside to the *** model provides the parameter conditions,i.e.,the internal and external forces are independent or ***,the case that the whole contact region of the spring belt has one subregion,two subregions,and three subregions is *** model gives a theoretical basis for the parameter optimization of spiral springs.

关键词： spiral spring simplified static model recursive method piecewise smooth feature

Energy evolution in complex impacts with friction

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Science China(Physics,Mechanics & Astronomy) 2013年第5期56卷 875-881页

作者： ZHANG HongJian liu caishan ZHAO Zhen BROGLIATO Bernard State Key Laboratory for Turbulence and Complex Systems College of EngineeringPeking University School of Aeronautic Science and Engineering Beihang University INRIA BIPOP project-teamZIRST Montbonnot655 avenue de l'EuropeSaint Ismier 38334France

In this paper, we base a theory established in an impulse-energy level to solve a problem of a disk-bail system, in which a moving ball collides perpendicularly against an disk staying on a horizontal surface. The impact process is an ensemble con- sisting of a point impact coupled with a line contact between bodies of the disk, the ball and the fixed horizontal surface. We experimentally and theoretically show that the post-impact states of the disk dramatically vary with the impacting position of the ball. Explanations are given by investigating the evolutions of the potential energies resided in the points involved in the complex frictional impacts. Good agreements between numerical and experimental results strongly suggest that the evolution of energy together with the dissipation must be reflected in mathematical models if a precise description for the post-impact state of systems is expected.

关键词： complex impact friction non-smooth mechanics disk-ball system experiments

Jump rule for edge impacts of rolling prisms

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Theoretical & Applied Mechanics Letters 2018年第6期8卷 425-430,I0006页

作者： Zhen Zhao Nannan Wang caishan liu School of Aeronautic Science and Engineering Beihang University State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University

We study experimentally and theoretically the planar dynamics of purely rolling prisms on a rough ramp, where the rolling motion is interrupted intermittently by edge impacts. The experiments were carried out for prisms made of different materials and having different geometries. We found that the angular velocities of the rolling prisms are material-independent, but they change significantly with their geometry. We modelled the dynamics of edge impacts by considering a socalled detachment front propagating across the contact interface. The detachment front represents the moving boundary between a detached region and a stress region that coexist within the interface plane. The theoretical analysis indicates that the detachment front can be characterized by a scale number, whose value converges to 0.4050 for prisms having large number of edges. A new jump rule for edge impacts is then developed, by which we can accurately reproduce the experimental observations, and explain why the motion of the prism is material-independent.

关键词： Surface impact Jump rule Experiments

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复合材料柔性空间机械臂振动特性分析

载人航天 2025年第1期31卷 44-51页

作者：王囡囡魏传彤刘才山山东建筑大学机电工程学院济南250101 北京大学工学院北京100871

针对复合材料空间机械臂在运动过程中柔性臂杆易产生强烈振动的问题,将空间机械臂简化为旋转刚体-薄壁梁模型,进行了中心转速、复合材料铺层方式以及横截面形状对复合材料柔性空间机械臂振动特性影响的研究。首先,根据复合材料的本构关... 详细信息

针对复合材料空间机械臂在运动过程中柔性臂杆易产生强烈振动的问题,将空间机械臂简化为旋转刚体-薄壁梁模型,进行了中心转速、复合材料铺层方式以及横截面形状对复合材料柔性空间机械臂振动特性影响的研究。首先,根据复合材料的本构关系,建立了复合材料薄壁梁的本构方程;然后,基于欧拉-伯努利梁理论和哈密顿原理,利用本构方程和旋转梁的运动学模型建立了梁的偏微分动力学方程,通过傅里叶变换将连续系统离散为多自由度系统,进而得到了梁的离散振动方程;最后,将振动方程无量纲化,通过数值计算求解薄壁梁的固有频率和模态。模态分析结果表明:固有频率会随中心转速的增大而变大,随铺层角度的增大而变小。此外,横截面锥度对复合材料旋转变截面薄壁梁振动特性起决定性作用,截面锥度的减小会增大固有频率,同时降低铺层角度对固有频率的影响。

关键词：旋转梁变截面固有频率复合材料