柔性机构非线性动力学问题的研究

柔性机构非线性动力学是先进设计技术中的重要研究领域之一，通过对二个实际的柔性机构的研究说明柔性机构非线性动力学的研究方法和研究内容，柔性机构非线性动力学是非线性动力理论与机械学的结合。     

谐波齿轮传动的含间隙机构的动力学分析

在考虑谐波齿轮柔性的基础上,研究了谐波齿轮传动对间隙机构动力学特性的影响。首先,利用非线性弹簧阻尼模型建立了谐波齿轮传动的含间隙机构的接触碰撞动力学模型。然后,对含间隙曲柄滑块机构进行仿真分析,结果表明谐波齿轮传动和机械部件柔性对间隙碰撞都有缓冲效果,只是机械部件刚度较大时,部件柔性的缓冲效果不明显,而降低机械部件刚度又将导致机械部件在运动过程中产生大变形,影响其机械性能。为谐波齿轮传动在含间隙机构中的应用,提供了理论依据。     

基于柔性多体动力学理论的舰船机械设备隔振系统建模

将柔性多体动力学理论应用于非线性隔振系统建模过程中,建立了线性弹性元件及非线性弹性元件的力学模型,利用该力学模型和单柔性体的动力学微分方程推导出了对舰船机械设备隔振系统动力学研究具有普适性的一般理论模型。     

基于熵权法的含间隙和柔性的机构定量分析方法及应用EI北大核心CSCD

含间隙机构运动过程中呈现出非线性,为了更好的模拟含间隙机构实际工况,对局部构件做柔性化处理,在建立间隙机构动力学模型的基础上,利用ADAMS二次开发功能,通过Fortran语言自主编写接触力的求解子程序,加载到ADAMS函数求解库中,实现接触模式实时判别和接触力的求解,分析考虑间隙和局部构件柔性对机构的运动特性影响规律。采用Lyapunov指数验证其运动非线性,并在此基础上提出一种基于熵权法的非线性定量分析新方法,通过MATLAB编写熵权法程序并对仿真结果进行定量分析,评估间隙和构件柔性对机构非线性的影响程度,并将该方法应用于2-RR&2-PR并联机构运动特性研究。结果表明:在任何条件下,动平台X方向加速度熵权值最大,说明对非线性影响权重最高,通过分析不同因素对机构非线性影响程度的趋势,使得对机构非线性程度的描述更为准确,为未来含间隙机构非线性定量分析提供了理论参考。     

受压旋转钻柱非线性动力学与分叉研究

在水平井钻井过程中,钻柱由于受压很容易发生横向振动,引发钻柱失效、井眼扩径等严重事故。该文将受压柔性旋转钻柱简化为柔性旋转梁,将钻柱受到的复杂载荷简化到柔性旋转梁系统中,基于vonKarman理论建立了柔性钻柱的动力学方程,再利用Galerkin法离散偏微分方程,得到了钻柱的非线性控制方程,并且利用多尺度法得到了平均方程。运用非线性动力学的方法分析柔性旋转梁在共振情况下的复杂动力学响应,得出系统中钻柱旋转角速度对非线性动力学响应的变化规律。研究结果可为水平井钻井过程中减少钻柱失效、提高钻速和降低钻井成本提供参考。     

柔性多体系统碰撞动力学研究

摘 要：针对工程中常见的柔性多体系统碰撞过程,详细的分析了柔性多体系统的接触碰撞条件,基于非线性等效弹簧阻尼模型建立了柔性体的碰撞模型,并基于库仑摩擦模型考虑两体碰撞时的切向摩擦作用。在此基础上把柔性体碰撞模型综合到柔性多体系统动力学方程中,建立了含接触碰撞的柔性多体系统动力学模型,此模型适用于一般含碰撞的多体系统。仿真算例以柔性梁在重力场中的接触碰撞过程为对象进行动力学仿真,研究柔性梁碰撞前、碰撞过程及碰撞后的动力学特性和动态响应,以及碰撞过程碰撞力的变化规律,并与刚性梁在重力场中的接触碰撞过程进行详细的比较和分析,结果表明基于非线性等效弹簧阻尼模型建立的柔性多体系统碰撞动力学模型可以有效的分析接触碰撞过程的动力学性能,验证了模型的有效性和正确性。     

多柔性体系统振动问题分析研究

在以往单柔性体系统振动研究和柔性多体系统动力学理论的基础上,对包含多个柔性体在内的机械系统振动响应进行分析。通过使用ANSYS和ADAMS软件建立以曲轴活塞机构为代表的系统动力学模型,然后使用柔性体代替机构中的不同部件进行振动响应比较计算的方法,得到系统中柔性体变化与系统整体振动响应变化之间的基本规律。这些规律能够为大型系统级振动分析模型的简化和计算精度保证提供必要的参考。     

基于ADAMS的连杆机构多体动力学仿真研究

以柔性连杆为研究对象,应用多体系统动力学对曲柄-滑块机构进行了仿真研究。基于ADAMS建立了机构的虚拟样机模型,利用动力学仿真得到高速、重载下连杆柔性对系统性能的影响;通过连杆的振动模态分析了系统性能变化的机理,并用有限元法对连杆的动应力分布进行了计算和分析,使得在结构设计阶段就可以预估机构的疲劳寿命,实现了机构的虚拟样机设计。     

空间站展开机构的失谐动态响应分析

考虑了动力失谐、质量失谐和摩擦失谐三种常见失谐现象,研究了空间站展开机构的失谐动态响应。利用多柔体系统动力学方法,在机械系统动力学自动分析(ADAMS)仿真平台下建立了空间站柔性展开机构的失谐模型,并用重要度抽样方法随机抽取失谐量,然后进行机构动学仿真,得到机构的失谐动态响应并进行统计。仿真研究证明,该方法可用较少的计算时间得到柔性展开机构的失谐动态响应随机分布特性。     

机械柔性结构的非线性动力学研究概述

随着现代工业的高速发展,机械结构不断向柔性化、轻质化和大型化的方向发展,机械柔性结构的动力学振动与控制问题的研究显得尤为重要。主要介绍弦和梁结构的非线性动力学研究现状,希望能为相关领域的研究起到铺垫作用。     

Buckling dynamics of imperfect Elastica subject to various loading conditions

Buckling dynamics of a pinned-pinned flexible imperfect beam attached to a sliding mass is investigated using nonlinear Elastica theory. Initially straight flexible buckling beam having pinned end boundary conditions loaded at one of its end with curved imperfection is considered. Large deflection analysis of flexible beam is studied using nonlinear Elastica theory. Imperfection analysis of the flexible beam is investigated considering the imperfection as an initial curvature. The governing differential equations are expressed in terms of nonlinear functions that are typical of flexible beams, generally leading to highly implicit relationships involving elliptic integrals and functions. Dynamic simulation of the flexible beam is studied using numerical simulation procedures with various types of loading (step, ramp, and sinusoidal) assuming this member buckles in its first mode. Dynamic response of the imperfect buckling Elastica has been obtained by using numerical Runge-Kutta methods. Load deflection characteristics of flexible beams are presented in polynomial curve fits. The polynomial curve fits obtained from nonlinear inextensible exact beam theory may then be used as the nonlinear lumped system stiffness. The buckling Elastica may find applications in compliant mechanism design. The motivation behind this research is not only to present the dynamic behavior of the buckling beam considering the magnitude of the imperfection but also to provide a tool to design new types of compliant mechanisms. Original compliant mechanism designs are presented demonstrating where the buckling dynamics of imperfect Elastica or flexible curved beams might be needed in mechanism design and synthesis.     

空间机器人柔性臂动力学建模,分析,控制与仿真的研究

空间机器人柔性臂是一个非常复杂的非线性，强耦合的动力学系统，其这的研究是比较复杂和困难的问题，本文对其建模，分析到控制与仿真等各个方面，结合国内外和发展的状况，综合性地进行了分析，并对一些需要重点解决的问题进行了较详细的研究与探讨，最后，指出了研究与发展的方向。     

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.     

Frequency-dependent fitness induces multistability in coevolutionary dynamics

Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a fundamental aim of theoretical research. Recent works quantitatively studied coevolutionary dynamics of competing species with a focus on linearly frequency-dependent interactions, derived from a game-theoretic viewpoint. However, several aspects of evolutionary dynamics, e.g. limited resources, may induce effectively nonlinear frequency dependencies. Here we study the impact of nonlinear frequency dependence on evolutionary dynamics in a model class that covers linear frequency dependence as a special case. We focus on the simplest non-trivial setting of two genotypes and analyse the co-action of nonlinear frequency dependence with asymmetric mutation rates. We find that their co-action may induce novel metastable states as well as stochastic switching dynamics between them. Our results reveal how the different mechanisms of mutation, selection and genetic drift contribute to the dynamics and the emergence of metastable states, suggesting that multistability is a generic feature in systems with frequency-dependent fitness.     

基于高斯基模糊神经网络的漂浮基柔性空间机械臂自学习控制

讨论了载体位置不受控、姿态受控情况下,自由漂浮柔性空间机械臂的高斯基模糊神经网络自学习控制问题。利用拉格朗日方程和模态综合法可建立柔性空间机械臂的动力学模型,但由于此类空间机器人系统严格遵守动量守恒,其动力学方程表现出强烈的非线性性质。结合神经网络和模糊控制,即利用神经网络来实现模糊推理可使模糊控制具有自学习能力,在此基础上,设计了柔性空间机械臂关节空间的高斯基模糊神经网络自学习控制方案。由于将动量守恒定理耦合到系统动力学方程的推导过程中,所提出的控制方案具有不需要测量、反馈载体位置、移动速度和移动加速度的显著优点。系统的数值仿真,证实了方法的有效性。     

Chaos computing: ideas and implementations

We review the concept of the 'chaos computing' paradigm, which exploits the controlled richness of nonlinear dynamics to obtain flexible reconfigurable hardware. We demonstrate the idea with specific schemes and verify the schemes through proof-of-principle experiments.     

模糊自抗扰控制器在挠性航天器振动抑制中的应用

针对挠性航天器在轨运动过程中挠性结构的持续振动问题,提出了一种基于模糊控制原理的改进型自抗扰控制方法,实现对挠性航天器的振动抑制。通过非线性自抗扰控制器快速地抑制挠性航天器的低频振动,并结合模糊控制实现自抗扰控制器(Auto Disturbance Rejection Controller, ADRC)参数的自整定,提高自抗扰控制器的性能。将仿真结果与PD控制和非线性自抗扰控制进行对比,结果表明该控制算法能更加快速有效地抑制挠性航天器的振动,具有重要的理论研究和工程应用价值。     

A Lagrange‐Euler‐assumed modes approach to modeling flexible robotic manipulators

Abstract

This paper presents a general Lagrange‐Euler‐assumed modes dynamics formulation for lightweight flexible manipulators. The proposed explicit form formulation, not yet available in the existing literature, can be viewed as an extended version of the Lagrange‐Euler formulation for rigid manipulators. The deformation of a link from its rigid body position is modeled by a homogeneous 4×4 transformation matrix composed of summations of assumed link modes. The number of modes can be arbitrarily selected. The joint flexibility is modeled by a linear torsionai spring with known characteristics. The methodology presented can be easily used to derive the full nonlinear dynamic equations of flexible manipulators by computing only the dynamic coefficients using computer algebra such as MACSYMA. The resulting nonlinear dynamic equations are in a closed form and are especially suitable for advanced nonlinear control strategy synthesis. Taken as an illustrative example, a two‐link flexible manipulator is studied to demonstrate the effectiveness of the formulation.     

Nonlinear wave scattering at the flexible interface of a granular dimer chain

Uncompressed granular dimer chains composed of repetitive pairs of heavy-light spherical, linearly elastic beads exhibit interesting intrinsic responses. The dynamics of these highly discontinuous nonlinear media is governed by the mass ratio scaling the mass disparity of each heavy-light pair of beads. In particular, it has been theoretically and experimentally shown that they support countable infinities of anti-resonances at a discrete set of mass ratios leading to solitary pulses propagating through the dimers with no attenuation or distortion. Conversely, they support countable infinities of resonances at a different discrete set of mass ratios, leading to substantial and rapid attenuation of propagating pulses due to energy scattering from low-to-high frequencies and wavenumbers by means of radiating traveling waves. In this work we computationally study nonlinear scattering of impeding pulses at the interface of an impulsively excited dimer chain with a dispersive elastic boundary, namely, a finite linear string resting on an elastic foundation. We develop a computational algorithm which, through iteration and interpolation at successive time steps, accurately computes (and ensures convergence of) the highly discontinuous contact forces and displacements at the flexible interface of the granular medium. This enables accurate computation of wave transmission, reflection, localization or multi-scale nonlinear scattering at the flexible interface for varying mass ratios of the dimer and the interface parameters. We show that, depending on the mass ratio of the dimer and the stiffness of the elastic foundation, the nonlinear scattering at the flexible interface may lead to significant reduction of the maximum contact force at the interface, and, thus, drastically affect the transmitted and reflected energy at the flexible boundary. In fact, an inverse relation between the stiffness of the elastic foundation and the residual energy transferred from the dimer chain to the flexible boundary is found. Moreover, for sufficiently small mass ratios of the dimer chain transient breathers are realized close to the interface in the form of localized “fast” oscillations of light granules of the dimer that entrap shock energy and then release in a slow time scale back to the chain and the flexible boundary. This work paves the way for studying highly discontinuous and nonlinear scattering phenomena at interfaces of granular media with flexible continua.