轴向运动梁横向非线性振动研究

应用增量谐波平衡法(IHB法)研究轴向运动梁横向非线性振动的内部共振．根据哈密顿原理建立非惯性参考系下轴向运动梁的横向振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程,再应用IHB法进行非线性振动分析,研究了在固有频率之比ω20／ω10接近于3：1情况下,外激励频率ω在ω10,ω20附近的具有内部共振的基谐波和次谐波响应．数值结果表明了IHB法是一个求解轴向运动体系非线性振动的非常有效的半解析、半数值的方法。     

轴向运动薄板非线性振动及其稳定性研究

应用增量谐波平衡法(IHB法)研究轴向运动薄板横向非线性振动特性及其稳定性.通过Hamilton原理推导出了非惯性参考系下四边简支轴向运动薄板的横向振动微分方程,然后利用Galerkin方法离散运动方程.对离散后的非线性方程组应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10附近的具有内部共振的基谐波响应.最后用多元Floquet理论分析了系统周期解的稳定性,其中采用Hsu方法来计算转移矩阵.通过对具体例子的数值计算,分别得到了自由振动和不同外激励下的频幅相应曲线,通过对比运动梁模型和运动薄板模型的计算结果,分析了各种模型的适用范围.     

复模态分析超临界轴向运动梁横向非线性振动

近似解析研究了简支边界条件下超临界轴向运动梁横向非线性自由振动的固有频率和模态函数.采用复模态方法处理控制方程,一个积分偏微分方程.将Galerkin截断思想用于近似处理线性化方程,一个含空间依赖系数的常微分方程.给出了不同截断项数对固有频率的影响.基于8项截断,讨论了系统参数对模态函数的影响.     

轴向运动梁横向非线性振动模型研究进展

综述了描述轴向运动梁横向非线性振动的两组数学模型的研究进展.在轴向运动梁径向和横向平面非线性振动耦合模型的基础上,总结了两组横向非线性振动模型的推导,以及在自由振动、受迫振动、参激振动工况下两组横向模型的近似解析比较的研究进展.在直接数值离散方法的基础上,总结了两组横向模型在各种工况下对平面耦合模型近似程度的研究进展.最后提出若干尚待深入研究的问题.     

索-梁耦合结构的分岔反控制研究

斜拉索是斜拉桥主要的支撑单元,是斜拉桥的重要组成部分.本文研究了控制增益参数G对索-梁耦合结构的振动控制.利用文献已得到的索-梁耦合结构的面内非线性运动微分方程,根据离散法,对其进行分离变量法处理,进而得到索-梁耦合结构的单自由度和两自由度模态方程.不同于以往的研究,本文假设索(梁)的左支撑点即坐标原点处是可以沿纵向方向自由移动的,则索的动态应变会发生改变,进而改变其模态方程一次项系数,通过这一规律可以在理论上转换得到一套状态控制反馈准则,并根据Floquet稳定性理论,将上述方程转换为Hill方程形式.然后通过摄动法,得到运动微分方程的稳定解.最后对索-梁耦合结构的单自由度和两自由度系统进行了数值分析计算,通过改变反馈控制增益系数,可以实现系统的反控制.而设计者可以通过这些复杂现象的参数变化范围设计选择合适的参数,尽量使得系统能在工程师所能控制的安全范围内振动.这种控制策略保持了系统的平衡,并且可以应用于在期望位置处具有最优稳定性的退化倍周期分岔.研究表示,无论结构是单自由度还是两自由度系统,反馈控制增益系数的变化能明显有效地改变系统的共振情形下的幅值.通过适当调整控制参数,能在预先...     

有限元法的轴向运动梁的激励功率谱辨识

主要考虑弯曲变形的细长轴向运动梁,可以作为工程中广泛应用在航天器天线、液体输送管道、汽车驱动带、电梯缆索等的简化机构.对轴向运动柔性梁线性微分方程,采用复模态分析方法导出两端简支和固支边界条件下的固有频率方程;采用Ritz法建立轴向运动梁的有限单元法模型.基于该模型在多种边界条件下进行梁的横向振动分析,并开展定点激励下激励功率谱的辨识.仿真结果表明,与传统的Galerkin截断方法相比.有限元方法能够克服分析方法的建模困难,对复杂边界梁进行有效的分析,对激励的功率谱能够有效地辨识.     

轴向运动功能梯度粘弹性梁横向振动的稳定性分析

基于Euler梁理论研究了轴向运动功能梯度粘弹性梁横向振动的稳定性问题.基于问题的数学模型和控制方程,利用微分求积法求得了轴向匀速运动功能梯度粘弹性梁亚临界区域内横向振动的复频率,分析其随着轴向运动速度、材料梯度指数等参数的变化情况,探讨上述参数对超临界区域失稳形式的影响.然后应用多尺度法结合边界条件分析了轴向速度带有周期扰动成分的变速运动功能梯度粘弹性梁的失稳问题,重点讨论了当速度扰动频率为固有频率二倍或者为两固有频率之和/差时所发生的次谐波共振及组合共振所导致的失稳.数值算例表明,随着梯度指数的增大,匀速运动功能梯度粘弹性梁的临界发散速度、耦合速度以及变速运动功能梯度粘弹性梁的稳定区域减小,且粘弹性系数的影响逐渐变弱,同等条件下,轴向运动功能梯度粘弹性固支梁比简支梁更为稳定.     

用微分求积法分析轴向加速粘弹性梁的非线性动力学行为

用微分求积数值方法求解了轴向加速粘弹性梁的横向振动控制方程,其方程是一复杂的非线性偏微分方程.并在数值结果的基础上利用分叉图分析了轴向定常加速度以及轴向加速度变化幅值对轴向加速粘弹性梁的非线性动力学行为的影响.     

受轴向激励弹性支承梁的稳定性分析

对于广泛存在的弹性支撑梁,首次呈现支承弹簧刚度对轴向激励下梁横向振动稳定性的影响.应用Hamilton原理,建立了两端由线性弹簧支撑的受轴向激励梁的动力学控制方程.通过解析方法计算了受轴向压力梁的固有频率,得到了支撑弹簧刚度与系统固有频率和临界轴力的关系.Galerkin截断后,通过多尺度法和Runge-Kutta法,计算得到了梁参激振动稳态响应的半解析与数值解.讨论了激励幅值、支撑弹簧刚度、平均轴力对系统非线性响应幅值及软硬特性的影响.利用Routh-Hurwitz稳定性判据,求得系统的参激稳定边界,着重讨论了支撑弹簧刚度、阻尼系数的影响.研究发现,边界支撑弹簧的刚度可以显著改变受轴向激励梁的参激稳定边界.因此,研究结果将为广泛存在受到轴向激励结构的设计提供指导.     

压电复合材料梁的全局分叉、混沌动力学分析

研究了简支压电复合材料层合梁在轴向、横向载荷共同作用下的非线性动力学、分叉和混沌动力学响应.基于yon Karman理论和Reddy高阶剪切变形理论,推导出了压电复合层合梁的动力学方程.利用Galerkin法离散偏微分方程,得到二个自由度非线性控制方程,并且利用多尺度法得到了平均方程.基于平均方程,研究了压电层合梁系统...     

轴向运动粘弹性夹层梁的横向振动

研究了小扰度下轴向匀速运动粘弹性夹层梁的振动模态和固有频率.基于Kelvin粘弹性本构方程,建立了轴向运动粘弹性夹层梁横向振动控制方程.分别采用Galerkin截断和复模态分析方法,研究两端简支的粘弹性夹层梁的固有频率和模态函数,讨论了轴向运动速度、夹心层与约束层厚度比、初始轴力等参数对夹层梁固有频率、临界速度及稳定性的影响.     

用微分求积法分析轴向移动粘弹性梁的非平面非线性振动

用微分求积法分析了轴向移动粘弹性梁非平面非线性振动的动力学行为.轴向移动粘弹性梁非平面非线性振动的数学模型是一非常复杂的非线性偏微分方程组.首先用微分求积法对其控制方程组进行空间离散,得到非线性常微分方程组,然后求解常微分方程组得到数值结果.在数值结果的基础上结合非线性动力学理论,利用分叉图、时间历程图、相图对其非线性动力学特性进行了分析.     

A Lagrange–Eulerian formulation of an axially moving beam based on the absolute nodal coordinate formulation

In the scope of this paper, a finite-element formulation for an axially moving beam is presented. The beam element is based on the absolute nodal coordinate formulation, where position and slope vectors are used as degrees of freedom instead of rotational parameters. The equations of motion for an axially moving beam are derived from generalized Lagrange equations in a Lagrange–Eulerian sense. This procedure yields equations which can be implemented as a straightforward augmentation to the standard equations of motion for a Bernoulli–Euler beam. Moreover, a contact model for frictional contact between an axially moving strip and rotating rolls is presented. To show the efficiency of the method, simulations of a belt drive are presented.     

Stability optimization of beams conveying fluid or carrying other axially moving materials

Optimal designs, and sensitivities of such designs, are calculated for transversely vibrating structures carrying an axially moving material. The structures studied consist of piecewise uniform and initially straight beam elements conveying a piecewise constant-speed plug flow of material along their deflected axes. The beams can be supported by a distributed Winkler-type ambient medium. Viscous damping in the beam material and the ambient medium is considered. Large static axial loads may act on the beam and on the moving material. The beams are modelled with a generalized second-order Rayleigh-Timoshenko theory including the Euler-Bernoulli theory as a special case. The structures investigated may also contain taut strings and rigid bodies. Considering a given subcritical material speed, the aim of the present study is to modify the initial design of a given beam structure in such a way that the transient vibrational motion following a transverse disturbance will die out as quickly as possible. To this end, complex eigenfrequencies pertaining to transverse vibration are calculated, and design parameters are changed so as to maximally raise the imaginary part of that eigenfrequency which has the smallest such part. In one of the examples, the objective is to maximally raise the product of the real and imaginary parts of the eigenfrequency which has the smallest such product.     

Multivariable Adaptive Control of the Rewinding Process of a Roll-to-roll System Governed by Hyperbolic Partial Differential Equations

In this paper, an active control scheme for the rewinding process of a roll-to-roll (R2R) system is investigated. The control objectives are to suppress the transverse vibration of the moving web, to track the desired velocity profile, and to keep the desired radius value of a rewind roller. The bearing coefficient in the rewind shaft is unknown and the rotating elements in the drive motor are various. The moving web is modeled as an axially moving beam system governed by hyperbolic partial differential equations (PDEs). The control scheme utilizes two control inputs: a control force exerted from a hydraulic actuator equipped with a damper, and a control torque applied to the rewind roller. Two adaptation laws are derived to estimate the unknown bearing coefficient and the bound of variations of the rotating elements. The Lyapunov method is employed to prove the robust stability of the rewind section, specifically the uniform and ultimate boundedness of all of the signals. The effectiveness of the proposed control schemes was verified by numerical simulations.     

Finite element analysis of air-sheet interactions and flutter suppression devices

A computational procedure is developed to analyze the vibration of an axially moving web, controlled through self-acting air bearings. The Galerkin finite element method is employed for the spatial discretization of both the moving web and thin air layers. The predictor-corrector method is also implemented along with the Newton-Raphson iteration for the time integration. It is shown that the pressurized air layers between the moving web and bearing surfaces can significantly reduce the transverse web deflection and provide a means of effective stabilizing. Some comparisons with results obtained using ADINA are presented. The computational algorithm introduced in this paper can be used to optimize both bearing-geometry designs and spatial locations.