Nonlinear dynamic analysis on rigid-flexible coupling system of an elastic beam

Previous work examined the effect of the attached stiffness matrix terms on stability of an elastic beam undergoing prescribed large overall motion. The aim of the present work is to extend the nonlinear formulations to an elastic beam with free large overall motion. Based on initial stress method, the nonlinear coupling equations of elastic beams are obtained with free large overall motion and the attached stiffness matrix is derived by solving sub-static formulation. The angular velocity and the tip deformation of the elastic pendulum are calculated. The analytical results show that the simulation results of the present model are tabled and coincide with the one-order approximate model. It is shown that the simulation results accord with energy conservation principle.

ANALYSES ON NONLINEAR COUPLING OF MAGNETO-THERMO-ELASTICITY OF FERROMAGNETIC THIN SHELL—II:FINITE ELEMENT MODELING AND APPLICATION

Based on the generalized vaxiational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established （see, Analyses on nonlinear coupling of magneto-thermo- elasticity of ferromagnetic thin shell--I）, the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDEMANEUVER STABILITY OF A COUPLEDRIGID-FLEXIBLE SYSTEM

The influences of nonlinear centrifugal force to large overall attitude motion of coupled rigid-flexible system was investigated. First the nonlinear model of the coupled rigid-flexible system was deduced from the idea of “centrifugal potential field', and then the dynamic effects of the nonlinear centrifugal force to system attitude motion were analyzed by approximate calculation; At last, the Lyapunov function based on energy norm was selected, in the condition that only the measured values of attitude and attitude speed are available, and it is proved that the PD feedback control law can ensure the attitude stability during large angle maneuver.

MODELING AND ANALYSIS OF A COUPLED RIGID_FLEXIBLE SYSTEM

Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of 'centrifugal potential field', which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius' method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

Stability of a Class of Coupled Rigid-elastic Systems With Symmetry-breaking

In this paper, the Poisson structures and Casimir functions, which play an important role in stability analysis of stationary motions, are given for a class of coupled rigid-elastic systems with symmetry-breaking. As a practical example, the specific Casimir function is given for a rigid-elastic coupled body with a fixed point subjected to gravitational force. At last, a set of sufficient conditions for stability of stationary motions of a rigid-elastic body in a circular orbit are given by the energy-Casimir method.

转子偏心效应下大范围转动弹性梁外激励非线性动力学行为与振动机制

为实现大范围转动弹性梁类柔性机械的高速、安全、平稳运行,综合应用Galerkin模态截断法和Hamilton原理建立弹性梁刚-柔耦合动力学模型,并建立转子偏心运动微分方程;基于行波叠加原理,应用高阶Runge-Kutta法完成非线性动力学解耦;应用时、频域分析法解析转子偏心效应下弹性梁的振动机制以及外激励下的频谱响应特性。研究结果表明:外激励响应在转子偏心效应下会衍生新的低频谐波分量,转速和激励幅值的增加会导致频域内多个低频谐波分量高于主振,易引发不同程度的间歇性振动;外激励频率提高会引起频域谱峰后移,数值仿真5~35 Hz频段的外激励,当频率为25 Hz时其低频谐波分量是主振幅值的2倍,高达0.181 mm,进而呈现明显的外激励突发性激振。因此,借助时、频域分析可有效解析具有随机性的间歇性或突发性振动产生机制,可为大型旋转柔性机械的动力学优化设计提供重要的理论基础和数据支持。

薄壁四点接触球轴承-腕部关节系统接触动力学分析

在机器人实际工况中,针对含有薄壁四点接触球轴承的机器人腕部关节系统的运动稳定性问题,对腕部系统模型进行了简化设计和仿真研究。在考虑薄壁结构的弹性变形和动态接触作用耦合影响的基础上,建立了刚柔耦合工业机器人腕部关节系统模型,分析了不同受载工况和正反转驱动下的变形规律和动态特性。首先,基于多体动力学和Hertz接触理论,设计了包含薄壁四点接触球轴承和中空轴及基座的腕部关节系统刚柔耦合接触动力学仿真模型;然后,考虑薄壁中空轴、基座、轴承套圈和保持架的结构弹性变形、钢球和套圈滚道、保持架的动态接触作用,研究了机器人腕部关节系统两种实际工况对保持架和钢球角速度、保持架和薄壁基座振动位移、钢球与套圈的动态接触力的影响;最后,计算分析了两种工况下腕部关节系统的动态载荷规律和振动响应特性。研究结果表明:在相对较大的径向载荷作用下,保持架和钢球会出现打滑现象,速度呈现周期波动,保持架和基座具有更好的运动稳定性,其薄壁轴承内部载荷降低,主副接触对均承担联合载荷,轴承内部载荷稳定性也更好。该仿真模型及结果可以为薄壁腕部关节系统的动力学分析与设计提供参考。

潮湿细粒煤炭筛分抗堵机理及参数优化研究

深部筛分是实现潮湿细粒煤高效分级的重要途径,但会出现筛面堵塞的问题,刚柔耦合弹性筛分方法被用于克服堵塞。探究了进料速率和物料含水率对筛分性能的影响及相关机理,对3 mm湿细粒煤进行刚柔耦合弹性筛分与刚性筛分对比实验,进一步明确了筛分过程中颗粒的空间分布规律。当外部含水率为11.31%时,筛分效率达到83.15%,总错配物率为6.40%,有效提高了潮湿细粒煤的筛分性能。

Application of Lagrange＇s equation to rigid-elastic coupling dynamics

A consistent focus in theoretical mechanics has been on how to apply Lagrange's equation to continuum mechanics.This paper uses the concept of a variational derivative and its laws of operation to investigate the derivation of Lagrange's equation,which is then applied to nonlinear elasto-dynamics.In accordance with the work-energy principle and the energy conservation law,kinetic and potential energies are proposed for rigid-elastic coupling dynamics,whose governing equation is established by manipulating Lagrange's equation.In addition,case studies are used to demonstrate the application of the proposed method to spacecraft dynamics.

Geometric nonlinear dynamic analysis of curved beams using curved beam element

Instead of using the previous straight beam element to approximate the curved beam,in this paper,a curvilinear coordinate is employed to describe the deformations,and a new curved beam element is proposed to model the curved beam.Based on exact nonlinear strain-displacement relation,virtual work principle is used to derive dynamic equations for a rotating curved beam,with the effects of axial extensibility,shear deformation and rotary inertia taken into account.The constant matrices are solved numerically utilizing the Gauss quadrature integration method.Newmark and Newton-Raphson iteration methods are adopted to solve the differential equations of the rigid-flexible coupling system.The present results are compared with those obtained by commercial programs to validate the present finite method.In order to further illustrate the convergence and efficiency characteristics of the present modeling and computation formulation,comparison of the results of the present formulation with those of the ADAMS software are made.Furthermore,the present results obtained from linear formulation are compared with those from nonlinear formulation,and the special dynamic characteristics of the curved beam are concluded by comparison with those of the straight beam.

HAMILTONIAN STRUCTURE FOR RIGID BODY WITH FLEXIBLE ATTACHMENTS IN A CIRCULAR ORBIT

Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular or- bit. At last, an example of stability analysis is given.

Geometric nonlinear formulation for curved beams with varying curvature

Based on exact Green strain of spatial curved beam, the relation for plane curved beam with varying curvature is derived nonlinear strain-displacement Instead of using the previous straight beam elements, curved beam elements are used to approximate the curved beam with varying curvature. Based on virtual work principle, rigid-flexible coupling dynamic equations are obtained. Physical experiments were carried out to capture the large overall motion and the strain of curved beam to verify the present rigid-flexible coupling formulation for curved beam based on curved beam element. Numerical results obtained from simulations were compared with those results from the physical experiments. In order to illustrate the effectiveness of the curved beam element methodology, the simulation results of present curved beam elements are compared with those obtained by previous straight beam elements. The dynamic behavior of a slider-crank mechanism with an initially curved elastic connecting rod is investigated. The advantage of employing generalized-or method is pointed out and the special nonlinear dynamic characteristics of the curved beam are concluded.

压电梯度板壳结构热电弹耦合建模与仿真

相比于复材层合结构,功能梯度材料不但能提供良好的比刚度,而且降低了分层损伤风险,结构梯度化是高性能结构发展的趋势。针对热电弹耦合下压电梯度结构,基于一阶剪切变形假设,构建了非线性温度梯度耦合下的压电梯度薄壁结构板壳有限元模型,实现高效的压电梯度结构“热-电-弹”耦合数值模拟。推导了压电梯度材料的“热-电-弹”耦合本构模型;假设温度梯度沿厚度方向呈二次变化,构建了2种非线性温度变化物理模型;基于一阶剪切变形假设,推导了多物理场耦合下的板壳有限元方程;采用商业有限元计算结构对本模型的准确性进行了验证,对压电梯度壳体结构进行了参数化仿真。

基于CFD/CSD耦合的高速射弹尾拍载荷特性研究

为提高射弹尾拍载荷的预测精度,建立了一套基于计算流体动力学(CFD)/计算结构动力学(CSD)双向耦合分析的计算方法和程序。射弹流体计算主控方程采用耦合SSTk-ω湍流模型和Schnerr-Sauer空化模型的Navier-Stokes方程,射弹结构计算采用基于模态叠加法简化的结构动力学方程,流固耦合界面插值采用径向基函数法,网格变形采用弹簧网格法。分别对泡型计算方法和流固耦合方法进行验证,在此基础上,计算对比1 000 m/s速度下射弹刚体和弹性体的尾拍泡型、结构变形和尾拍流体载荷特性差异。计算表明:弹性体尾拍过程,射弹泡型会产生弹身“二次拍击”、“局部沾湿”和沾湿面积增大等特殊现象,结构变形由弹性一弯模态主导,较大的变形引起流体载荷增大27%~105%,尾拍姿态角增大13%,尾拍频率增加20%,流固耦合效应对尾拍泡型、尾拍载荷和尾拍弹道均产生了较强的影响。

刚柔耦合关节SCARA机器人的双柔性动力学模型

针对电子装配机器人高速高精要求,提出一种能够利用柔性铰链变形补偿轴承摩擦死区,实现高精度定位运动的刚柔耦合关节SCARA机器人的概念设计,并建立考虑柔性铰链变形与机械臂一阶弹性变形的双柔性动力学模型。首先,设计一种刚柔耦合轴承的结构,通过轴承中柔性铰链的变形量主动补偿摩擦死区引起的定位误差;在每个关节处引入两个扭转弹簧,分别模拟柔性铰链和机械臂的弹性变形;其次,建立关节的摩擦模型以模拟关节摩擦环境;然后,使用拉格朗日动力学方法建立包含摩擦信息与振动信息的动力学模型。设计开环和闭环的数值仿真进行验证,结果表明该模型理论分析的有效性。

基于磁机械效应的铁磁材料漏磁检测数值模拟

为更准确地描述材料的非线性磁机械耦合效应,以非线性磁致伸缩应变方程、有效场理论和能量平衡方程等为基础提出新的磁弹性耦合模型与变刚度模型,分析了铁磁材料的磁机械效应和变刚度效应,并利用数值分析软件将非线性磁化模型的理论结果与仿真过程进行耦合。结果表明,仿真得到的缺陷泄漏场分布与已有研究结果一致,验证了所提出模型与仿真方法的可行性和准确性。分析了应力、缺陷尺寸和缺陷位置对表面磁场的影响,结果表明:在拉伸载荷作用下,试样表面法向磁场信号呈类S形曲线,切向信号呈类锥形曲线,其极值均随载荷增加先减小后增大;试样存在缺陷时,不同采集路径上获取的信号存在很大差异,缺陷边缘路径上的漏磁场峰值与缺陷长度呈负相关,而峰值距离和跨度却相反,在远离缺陷的采集路线上,漏磁场信号的峰值和跨度均与缺陷长度呈正相关。

弹性转子油气混输泵的非线性动力学研究

为了研究弹性体转子外表面橡胶非线性变形对弹性体转子泵的影响,采用非线性单向流固耦合方法,建立转子啮合接触有限元模型,将非定常计算结果内流压力载荷施加到转子表面,研究圆弧转子型线和宽头刮边转子型线在不同的橡胶壁厚和出口压力下,对转子泵效率和启动扭矩的影响.结果表明,无论采用哪种型线,压差对橡胶剪应力和变形量影响较大,而转动角度对剪应力峰值影响较小;剪应力较大值主要出现在转子与衬套、转子与转子接触点附近靠高压区侧的圆弧区;壁厚与最大剪应力和橡胶变形呈正相关.设计的螺杆转子和得到的数据可用于弹性转子油气混输泵的设计和优化,延长弹性体转子油气混输泵在深海环境下的使用寿命,并大大节省了维护成本.

扣件弹性垫层劣化对高速列车-道岔系统动力特性的影响

随着高速铁路运营时长的增加,道岔区扣件弹性垫层会发生劣化,对列车过岔的动力学性能产生不利影响。为研究扣件弹性垫层劣化对高速列车道岔系统动力特性的影响,考虑道岔区钢轨的柔性变形,以高速铁路18号无砟道岔为研究对象,建立车辆-道岔刚柔耦合动力学模型,通过时域和频域分析,研究扣件弹性垫层劣化位置、劣化程度、劣化个数及行车速度对列车道岔系统动力特性的影响。研究结果表明:扣件弹性垫层劣化位置影响较大,其中尖轨顶宽40 mm处为扣件弹性垫层劣化的最不利位置;随劣化程度的增加,车岔系统各动力学指标呈增大趋势,其中垂向指标影响更为显著;扣件弹性垫层劣化个数的增加对尖轨尖端的横向动力学指标产生不利影响,9组扣件连续劣化时横向力较1组扣件弹性垫层劣化时增大21.3%;当车辆以250 km/h速度过岔时,扣件弹性垫层劣化对列车道岔系统动力特性的影响最为显著。轴箱振动加速度对扣件弹性垫层劣化较敏感,可在一定程度上反映扣件弹性垫层的劣化。研究成果可为道岔区刚度优化和养护维修提供一定的理论指导。

适用于弹性飞机飞行动力学仿真的气动力降阶方法

针对低速太阳能无人机在由阵风引起的大迎角非线性气动力情况下的高精度、高效率气动弹性及飞行动力学工程仿真问题,对气动力降阶方法及其在飞行动力学仿真中的应用进行深入探索。以二维翼型为例,分别基于自回归外部输入模型(ARX)方法、多小波Volterra级数方法、反向传播(BP)、径向基函数(RBF)神经网络方法和支持向量回归(SVR)方法建立了非定常气动力降阶模型,并比较了5种方法的收敛性及泛化能力。在此基础之上综合ARX和神经网络方法的优点提出一种计算精度高,收敛性、泛化能力较强的ARX-BP/RBF组合建模方法。将基于ARXRBF的组合气动力降阶方法和弹性飞机刚弹耦合动力学方程相结合建立基于气动力降阶的弹性飞机飞行动力学仿真模型。以一架太阳能无人机模型为例,开展数值验证,对算例对象在阵风及舵面激励下的响应进行仿真研究,并和计算流体力学(CFD)-计算结构动力学(CSD)结果及基于线性气动力的仿真结果进行对比。结果表明:所建立的弹性飞机仿真模型能有效反映气动力非线性特性,且仿真效率高于CFD-CSD分析方法,适用于工程实践。

带非对称阻尼器的柔性支撑框架主余震作用分析

研究主余震耦合作用下具有非对称弹塑性特征的非对称摩擦阻尼器(asymmetrical friction damper, AFD)对柔性支撑框架结构的减震作用。传统扁钢柔性支撑(tension-only brace, TOB)存在松弛问题导致柔性支撑结构在主余震耦合作用下性能严重退化。研究表明:AFD适用于柔性支撑结构,具有非对称弹塑性特征,静摩擦阶段发挥非线性“自拉紧”效应,提供较大的恢复力;在滑动摩擦阶段提供稳定的附加阻尼。该研究对静摩擦阶段和滑动摩擦阶段分别给出了简化模型,对滑动摩擦阶段给出附加阻尼比计算方法,提出了基于AFD的拉紧保护模式和阻尼耗能模式。对比分析柔性支撑框架结构TOB方案和2种AFD方案的主震和主余震耦合弹塑性时程反应,TOB方案在中震主余震及大震主震下屈服,而在大震主余震分析下松弛导致结构破坏,证实柔性支撑结构在主余震耦合作用下存在较大风险;而2种AFD方案可有效保护结构,拉紧保护模式为结构提供更高的减震上限,阻尼耗能模式同样有效防止TOB过度松弛,在主余震作用下提升结构减震性能。