柔性多体系统动力学的若干热点问题

全面综述了柔性多体系统动力学近年来的研究成果．对建模方法、模态选取及模态综合、动力刚化及柔性多体系统动力学中微分－代数方程的数值方法等研究热点进行了详细的阐述,并简要展望了柔性多体系统动力学今后的发展趋势      

动力刚化与多体系统刚—柔耦合动力学

首先指出当前柔性多体系统动力学的大量工程研究背景,在回顾柔性多体系统动力学研究进展后指出动力刚化的现象揭示了刚－柔耦合的零次建模方法的局限,认为进一步深入进行柔性多体系统刚－柔耦合动力学的研究是多体系统动力学研究的新阶段,文末提出了刚－柔耦合动力学的研究任务。     

旋转运动柔性梁的假设模态方法研究

采用假设模态法对旋转运动柔性梁的动力特性进行研究，给出简化的控制模型. 首先采用Hamilton原理和假设模态离散化方法，在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下，推导出基于柔性梁变形位移场一阶完备的一次近似耦合模型，然后对该模型进行简化，忽略柔性梁纵向变形的影响，给出一次近似简化模型，最后将采用假设模态离散化方法的结果与采用有限元离散化方法的结果进行了对比研究. 研究中考虑了两种情况：非惯性系下的动力特性研究和系统大范围运动为未知的动力特性研究. 研究结果显示，当系统大范围运动为高速时，在假设模态离散化方法中应增加模态数目，较少的模态数目将导致较大误差. 一次近似简化模型能够较好地反映出系统的动力学行为，可用于主动控制设计的研究.     

平动弹性梁的刚-柔耦合动力学

本文建立了作大范围平动弹性梁的刚-柔耦合动力学控制方程。分析了大范围平动对弹性梁变形运动动力学性质的影响，发现了大范围平动与变形运动之间的耦合动力学与大范围转动与变形运动之间的耦合动力学存在显著的差异。大范围平动使弹性梁的刚度降低，同时使系统阻尼增加；而大范围转动使弹性梁的刚度增加，同时使系统产生了能量转换的陀螺效应。因此，柔性多体系统刚-柔耦合动力建模中必须包括大范围平动与柔性体变形运动之间的耦合动力学效应。     

基于旋转软化的柔性梁动力学研究

建立了旋转柔性梁的非线性动力学模型,利用能量法及哈密顿原理导出了耦合的动力学方程,分析了转动惯性、Coriolis力、应力刚化、旋转软化、加速度、横向位移、弯曲刚度等作用效应;通过设置应力刚化及旋转软化等刚度矩阵和编制有限元程序,建立了梁单元有限元模型,对柔性梁在旋转软化状态下的振动模态进行了数值模拟与分析。计算表明:梁的旋转软化导致其沿旋转平面的弯振模态(摆振)频率随转速增大而相对下降,且对第一阶摆振频率的影响最显著,呈现非线性;梁的旋转软化对垂直于旋转平面的弯振频率几乎没有影响,此结果表明了旋转柔性梁动态特性的复杂性,因此在计算旋转柔性梁的振动特性时,必须同时设置平动、转动惯性质量矩阵,才能获得准确结果。此外,梁单元模型与实体单元模型计算结果误差小于等于5%,验证了本文梁单元模型求解方法的准确性。     

单杆柔性机械臂的控制仿真研究

本文应用模态控制理论，对柔性机械臂的主动控制问题中的动力学模型进行了研究。在小变形假设的前提下，考虑由于横向变形而引起的轴向位称位的影响，采用拉格朗日方程建立了计及动力刚化项的动力学模型，并将ＰＤ控制理论和方法应用于刻模型。最后，对一单杆柔性机械臂的振动控制进行了计算机仿真．     

动力刚化多体系统动力学

本文利用几何非线性的应变－－位移关系，在小变形假设条件下，得到了一般柔性构件弹性有的广义价值标二阶小量表达式。在此基础上，利用Ｋａｎｅ方程的Ｈｕｓｔｏｎ方法，在推导偏（角）速度表达式后，作适当的线性化处理，以使动力刚度项得以保留，从而建立了动力刚化多体系统的动力学方程，仿真算例证明了该理论的正确性和有效性。     

作大范围运动弹性梁的动力刚化分析

刚体大范围运动与弹性梁的变形运动的相互耦合将产生动力刚化现象，在经典的动力学理论中无法解释这种现象。本文给出了该系统的运动描述方法，利用Ｈａｍｉｌｔｏｎ变分原理建立了动力学控制方程，利用Ｇａｒｌｅｒｋｉｎ模态截断研究了产生动力刚化的原因及其动力学性质，从本质上解释了学者们多年来一直在研究的动力硬化现象，最后用数值模拟验证了理论的正确性。本文所得结论有益于柔性多体系统动力学的发展。     

考虑刚弹耦合作用的柔性多体连续系统动力学建模

基于Ｈａｍｉｌｔｏｎ原理建立起一般柔性体连续系统的动力学建模方法,进而以水平面内作大范围回转运动的柔性梁为例,在Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ梁模型的假设前提下,根据轴向不可伸长的柔性梁的几何约束条件;推导出作大范围刚体运动的柔性梁连续系统的一致线性化振动微分方程．采用假设模态法对其离散化,导出考虑刚弹耦合作用的柔性梁有限维离散化动力学模型．最后给出仿真算例,验证了该方法的有效性．     

基于假设模态加权的全局模态提取方法及其应用

假设模态法在单一梁、杆、索、板等柔性结构动力学建模中有广泛应用，但在处理组合结构振动问题时，常常因无法反映各部件之间的耦合作用使其应用受限。通过假设模态建立组合结构的近似动力学模型，利用近似模型求得系统的固有频率和相应的特征向量，据此可以有效地获得系统的全局模态。本文以跨中带有多个弹性支撑的简支梁为例，通过假设模态加权来提取系统的全局模态，从而建立系统的动力学模型。对系统进行固有特性分析的结果表明，通过假设模态加权可以方便地获得系统的全局模态；对系统动态响应分析的结果表明，采用本文提出的全局模态建立的非线性动力学模型可以有效地反映系统的非线性动力学特性。     

DYNAMIC BEHAVIOR OF THIN RECTANGULAR PLATE ATTACHED TO MOVING RIGID

A nonlinear dynamic model of a thin rectangular plate attached to a moving rigid was established by employing the general Hamilton's variational principle. Based on the new model, it is proved theoretically that both phenomena of dynamic stiffening and dynamic softening can occur in the plate when the rigid undergoes different large overall motions including overall translational and rotary motions. It was also proved that dynamic softening effect even can make the trivial equilibrium of the plate lose its stability through bifurcation. Assumed modes method was employed to validate the theoretical result and analyze the approximately critical bifurcation value and the post-buckling equilibria.     

Modal test and analysis of cantilever beam with tip mass

The phenomenon of dynamic stiffening is a research field of general interest for flexible multi-body systems. In fact, there are not only dynamic stiffening but also dynamic softening phenomenon in the flexible multi-body systems. In this paper, a non-linear dynamic model and its linearization characteristic equations of a cantilever beam with tip mass in the centrifugal field are established by adopting the general Hamilton Variational Principle. Then, the problems of the dynamic stiffening and the dynamic softening are studied by using numerical simulations. Meanwhile, the modal test is carried out on our centrifuge. The numerical results show that the system stiffness will be strengthened when the centrifugal tension force acts on the beam (i.e. the dynamic stiffening). However, the system stiffness will be weakened when the centrifugal compression force acts on the beam (i.e. the dynamic softening). Furthermore, the equilibrium position of the system will lose its stability when the inertial force reaches a critical value. Through theoretical analysis, we find that this phenomenon comes from the effect of dynamic softening resulting from the centrifugal compression force. Our test results verify the above conclusions and confirm that both dynamic stiffening and softening phenomena exist in flexible multi-body systems. The project supported by the National Natural Science Foundation of China (19972002) and the Doctoral Programme from The State Education Commission China (20010001011)     

Dynamic characteristic and stability analysis of a beam mounted on a moving rigid body

The phenomenon of dynamic stiffening has drawn general interest in flexible multi-body systems. In fact, approximately analytical, numerical and experimental research have proved that both dynamic stiffening and dynamic softening can occur in flexible multi-body systems. In this paper, the nonlinear dynamic model of a beam mounted on both the exterior and the interior of a rigid ring is established by adopting the general Hamiltons variational principle. The dynamic characteristics of the system are studied using a theoretical method when the rigid ring translates with constant acceleration or rotates steadily. The research proves theoretically that both dynamic stiffening and dynamic softening can occur in both the translation as well as the rotation state of multi-body systems. Furthermore, the approximate vibration frequency, critical value and post-buckling equilibria of the translational beam with constant acceleration are obtained by employing the assumed modes method, which validates the theoretical results. The L² norm stability of the trivial equilibrium of the system with the external beam and the L norm stability of the bending of the external beam are proved by employing the energy–momentum method.This research was supported by the National Natural Science Foundation of China (10272002) and the Doctoral Program from the Ministry of Education of China (20020001032).     

Dymamics of a rotating flexible manipulator with tip load

The dynamics of a flexible manipulator is investigated in this paper. From the point of view of dynamic blance, the motion equations of a rotating beam with tip load are established by using Hamilton's principle. By taking into account the effects of dynamic stiffening and dynamic softening, the stability of the system is proved by employing Lyapunov's approach. Furthermore, the method of power series is proposed to find the exact solution of the eigenvalue problem. The effects of rotating speed and tip load on the vibration behavior of the flexible manipulator are shown in numerical results. Supported by National Natural Science Foundation. of China     

线性变厚度粘弹性矩形板在随从力作用下的动力稳定性

利用粘弹性微分型本构关系和薄板理论,对线性变厚度粘弹性矩形薄板建立了在切向均布随从力作用下的运动微分方程,采用微分求积法研究了在随从力作用下线性变厚度粘弹性矩形薄板的稳定性问题,具体对对边简支对边固支和三边简支一边固支条件下体变为弹性、畸变服从Kelvin-Voigt模型的变厚度粘弹性矩形板在随从力下的广义特征值问题进行了求解,分析了薄板的长宽比、厚度比及材料的无量纲延滞时间的变化对随从力作用下矩形薄板的失稳形式及相应的临界荷载的影响.     

匀速转动内悬臂梁稳定性研究

本文采用了凯恩简化模型并提出大范围平动和转动共同作用下的连续体梁模型;通过两种模型分析了匀速转动内悬臂梁的稳定性;指出了匀速转动内悬臂梁存在动力柔化现象,动力柔化的原因在于梁的大范围平动;提出了匀速转动内悬臂梁的内转半径和外转半径的概念,指出匀速转动内臂梁的内转半径和外转半径比值存在一定关系时,系统为一阶稳定,研究表明,同时作大范围平动和转动的柔性梁存在柔化和刚化的分界点,需要在实际应用中予以注意。     

径向基点插值法在旋转柔性梁动力学中的应用

将无网格径向基点插值法用于旋转柔性梁的动力学分析. 利用无网格方法对柔性梁的变形场进行离散,考虑梁的纵向拉伸变形和横向弯曲变形,并计入横向弯曲变形引起的纵向缩短,即非线性耦合项,运用第二类拉格朗日方程推导得到系统刚柔耦合动力学方程. 将无网格径向基点插值法的仿真结果有限元法和假设模态法进行比较分析,说明假设模态法的局限性,并表明其作为一种柔性体离散方法在刚柔耦合多体系统动力学的研究中具有可推广性,并讨论了径向基形状参数的影响. 同时运用3 种求解系统动力学方程的方法:纽马克方法、4阶龙格库塔法、亚当姆斯预报校正法,并比较各方法的计算效率, 结果表明纽马克方法最快.      

Transverse vibration characteristics of axially moving viscoelastic plate

The dynamic characteristics and stability of axially moving viscoelastic rect- angular thin plate are investigated.Based on the two dimensional viscoelastic differential constitutive relation,the differential equations of motion of the axially moving viscoelastic plate are established.Dimensionless complex frequencies of an axially moving viscoelastic plate with four edges simply supported,two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method.The effects of the aspect ratio,moving speed and dimensionless delay time of the material on the trans- verse vibration and stability of the axially moving viscoelastic plate are analyzed.     

Nonlinear vibration analysis of isotropic plate with inclined part-through surface crack

The four modes of vibration of an isotropic rectangular plate with an inclined crack are investigated. It is assumed that the crack remains continuous and its center is located at the center of the plate. The governing nonlinear equation of the transverse vibration of the plate with the plate boundary conditions being simply-supported on all edges is developed. The multiple scale perturbation method is utilized as the solution procedure to find the steady-state frequency response equations for all the four modes of vibration. The equations for the free and forced vibrations are derived and their frequency responses are presented. A special case of large-scale excitation force has also been considered. The parameter sensitivity analysis for the angle of crack, length of crack and the position of the external applied excitation force is performed. It has been shown that according to the aspect ratio of the plate, the vibration modes can have either nonlinear hardening effect or nonlinear softening behavior.     

Geometric nonlinear formulation and discretization method for a rectangular plate undergoing large overall motions

In the present paper, the geometric nonlinear formulation is developed for dynamic stiffening of a rectangular plate undergoing large overall motions. The dynamic equations, which take into account the stiffening terms, are derived based on the virtual power principle. Finite element method is employed for discretization of the plate. The simulation results of a rotating rectangular plate obtained by using such geometric nonlinear formulation are compared with those obtained by the conventional linear method without consideration of the stiffening effects. The application limit of the conventional linear method is clarified according to the frequency error. Furthermore, the accuracy of the assumed mode method is investigated by comparison of the results obtained by using the present finite element method and those obtained by using the assumed mode method.