非线性轴向运动黏弹性Rayleigh梁受迫振动的微分求积法

研究了轴向运动黏弹性Rayleigh梁的非线性受迫振动。运用广义Hamilton原理推导出梁和边界条件的非线性控制方程。通过复模态法计算固有频率和模态函数。运用多尺度法获得主共振的稳态响应,根据Routh-Hurwitz分析稳态响应的稳定性,同时得到粘性阻尼,力和非线性系数的影响曲线。如果存在不稳定区域,通过增加粘性阻尼或减小力可使稳态响应的稳定。运用微分求积法对轴向黏弹性梁的受迫振动进行数值分析,并与多尺度分析进行对比,以此来证明了多尺度法的结果的正确性。     

船用离心风机内部流动诱发蜗壳振动的数值研究

针对船用离心风机内部非定常流动诱发蜗壳结构振动响应,发展了一种数值计算方法,该方法首先通过风机内部非定常流场计算获得振动激励源,其次采用流固弱耦合算法实现节点的插值和载荷加载,最后基于有限元的模态叠加法得到蜗壳结构动力响应。流场压力脉动和振动计算结果和实验测试结果分别做了对比,结果吻合较好,表明本文的方法能较准确地模拟叶轮机械内部流动诱发外部壳体的振动响应。从流场和振动响应两个方面阐述了流动诱发振动的机理:基频的非定常气动力是流固耦合振动的主要激励源,基频分量在振动的频率响应函数中占据主导地位,蜗壳的最大振动响应是基频下的非定常气动力和基频振动模态共同作用的结果。     

不同边界条件下旋转薄壁短圆柱壳的强迫振动响应计算

为计算不同边界条件下旋转薄壁短圆柱壳的强迫振动响应特性,在总结前人所提出的两端简支边界条件下旋转有限长圆柱壳自由振动和谐波激励响应计算方法基础上,基于梁函数法,在位移函数的轴向引入含有不同边界条件特征的模态函数,从而得以求解。基于Love壳体理论,利用Harnilton原理建立了旋转薄壁短圆柱壳的振动微分方程,并利用Galerkin法进行离散简化为常微分方程。以简谐激励为例给出了一种以广义坐标形式表示的响应求解方法,由此求解出不同边界约束的旋转薄壁短圆柱壳的响应问题。通过试验对所提出响应计算方法的正确性进行了验证。     

黏弹性梁弯曲振动的复模态分析

发展复模态分析研究黏弹性梁的弯曲振动。将梁的控制方程写作状态变量的形式，然后利用复模态的正交性可解耦为无穷多个彼此独立的常微分方程组。基于固有频率和模态函数，可以得到黏弹性梁对于任意初始条件和外激励的响应。在固支梁的边界条件下确定黏弹性梁的固有频率、衰减系数和模态函数，并计算梁受两种典型的外激励时的响应。     

基于时间谱元法的动态响应优化

机械系统动态响应优化设计有很好的应用前景.动态响应必须满足依赖于时间的微分方程.为了获得最优解且满足与时间有关的约束,要求获得整个时间上的响应.研究基于时间谱元法的系统动态响应设计.深入探讨在时间域内离散动态响应,将运动微分方程组转化成代数方程组,精确解出瞬态响应,用高斯罗巴托勒让德(Gauss-Lobatto-Legendre,GLL)点法和关键点法处理时间约束.以最简单的多自由度动力学设计问题--2自由度弹簧减振器设计为例,引入人工设计变量,详细分析两种处理约束方法的优缺点,也说明此方法的正确性.这些内容可为进一步研究机械零部件的动态优化设计问题以及动载荷弹性分布参数系统的优化设计奠定基础,比如在固定端承受振动输入的矩形变截面梁的动态优化设计,在不同边界条件下承受垂直平面均布瞬态动载荷作用的弹性梁的动态优化设计等.     

轴向运动Timoshenko梁固有频率的求解方法研究

研究两端铰支边界条件下Timoshenko模型轴向运动梁的横向振动问题,分别利用复模态分析方法和Galerkin方法求解系统的固有频率;讨论轴向运动梁前两阶固有频率随轴向运动速度的变化情况;最后给出数值算例,分析复模态分析方法、二阶Galerkin截断和四阶Galerkin截断方法对固有频率结果精确度的影响.     

偏微分方程与微分代数方程的一致求解方法

Modelica 语言是一种复杂物理系统多领域统一建模语言,但目前该语言只能解决由微分代数方程（DAE）描述的问题,而不能解决由偏微分方程（PDE）表达的问题。为此,提出一种偏微分方程与微分代数方程的一致求解方法,利用所构建的径向基函数配点无网格法直接将偏微分方程在空间上离散成一系列的微分代数方程,然后采用成熟的微分代数方程求解器进行求解。实例结果表明,该方法在不改变 Modelica 语法的前提下,能较好地实现偏微分方程与微分代数方程的一致求解,且求解精度高、边界条件处理简单,有利于Modelica直接求解复杂工程系统中多领域耦合、时间域与空间域耦合的复杂问题。     

货车转向系统结构振动特性测试与优化

针对某型车开展了转向系统结构的动力学分析并进行了试验研究;采用瞬态激励测量转向系统结构的振动响应,得到加速度频响函数曲线;通过锤击法识别出转向盘、转向柱组件和汽车仪表板横梁管梁的约束模态参数。综合分析了模态振型和安装点动刚度,确定了需要优化的结构;通过对转向盘控制点的振动灵敏度测试,验证了优化方案的有效性。     

立式加工中心整机动态特性的测试与分析

系统地阐述了与有限元法相结合的模态试验分析方法。首先利用ANSYS Workbench对加工中心进行有限元模态分析,根据模态分析结果和具体情况布置模态试验激振点和测振点,然后采用单点激励多点响应模态试验分析方法来获取完整模态参数,引入相干性函数分析测试信号的可靠性。最后通过模态试验结果和有限元计算结果对比分析,准确识别出加工中心关键振型的模态参数,为加工中心的动态优化设计提供可靠的基础。     

基于曲率模态与柔度曲率的损伤识别

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。     

Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces

The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

     

Natural frequencies of Euler-Bernoulli beam with open cracks on elastic foundations

A study of the natural vibrations of beam resting on elastic foundation with finite number of transverse open cracks is presented. Frequency equations are derived for beams with different end restraints. Euler-Bernoulli beam on Winkler foundation and Euler-Bernoulli beam on Pasternak foundation are investigated. The cracks are modeled by massless substitute spring. The effects of the crack location, size and its number and the foundation constants, on the natural frequencies of the beam, are investigated.     

纤维增强FGM梁的自由振动和临界屈曲载荷分析

基于经典梁理论（CBT）研究轴向力作用下纤维增强功能梯度材料（FGM）梁的横向自由振动和临界屈曲载荷问题。首先考虑由混合律模型来表征纤维增强FGM梁的材料属性,其次利用Hamilton原理推导轴向力作用下纤维增强FGM梁横向自由振动和临界屈曲载荷的控制微分方程,并应用微分变换法（DTM）对控制微分方程及边界条件进行变换,计算了纤维增强FGM梁在固定-固定（C-C）、固定-简支（C-S）和简支-简支（S-S）3种边界条件下横向自由振动的无量纲固有频率和无量纲临界屈曲载荷。退化为各向同性梁和FGM梁,并与已有文献结果进行对比,验证了本文方法的有效性。最后讨论在不同边界条件下纤维增强FGM梁的刚度比、纤维体积分数和无量纲压载荷对无量纲固有频率的影响以及各参数对无量纲临界屈曲载荷的影响。     

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bernoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method (DTM) has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.     

Adaptive vibration control of micro-cantilever beam with piezoelectric actuator in MEMS

This paper proposes a dynamical model and the governing equations of motion of the micro-cantilever beams based MEMS with piezoelectric actuator (PZT). The Rayleigh–Ritz method is used to reduce the order of the system and the state equations are presented in modal space. The first ten mode frequencies and mode shapes of the micro-cantilever beam with and without PZT are studied. The effects of PZT on the modal frequencies and shapes of the beam system can be ignored for the reason that the beam holds larger nature frequencies and Q values in micro-scale. A rational linearizing feedback controller with a high gain observer is designed to eliminate the unwanted deflection of the micro-cantilever beam system. The open-loop step response and the effects of situated places of PZT on the frequency responses of the system are discussed. Various frequency responses of the beam system, subject to different applied control voltages and feedback gains, are illustrated. The four resonances are well controlled, while the anti-resonance has little change. Computer simulations are provided to demonstrate the performance of the designed control scheme.     

轴向运动功能梯度梁的横向振动

新型非均匀复合材料,功能梯度材料具有防止脱层和减缓热应力等优良性能,将其应用于功能梯度梁的结构有着非常重要的工程应用价值。基于Euler-Bernoulli梁理论和Hamilton原理,建立轴向运动功能梯度梁横向自由振动的运动微分方程,其中假设功能梯度梁的材料特性沿梁厚度方向按各组分材料体积分数的幂函数连续变化;再对运动微分方程和边界条件进行量纲一处理,采用微分求积法对其进行离散化,导出系统的广义复特征方程,然后计算分析轴向运动功能梯度简支梁横向振动复频率的实部和虚部随量纲一轴向运动速度、梯度指标等参数的变化情况,并讨论量纲一轴向运动速度和梯度指标对功能梯度梁的横向振动特性以及失稳形式的影响。     

大挠度后屈曲倾斜梁结构的非线性力学特性

基于弹性梁的几何非线性大挠度屈曲理论,建立两端固定对称倾斜支撑梁结构的大挠度后屈曲控制微分方程,采用几何非线性隐式变形协调关系来表达强非线性超静定边值问题,得到描述倾斜梁大挠度后屈曲行为的精确解析解.采用数值方法求解含有第一、二类椭圆积分的强非线性微分方程,给出不同倾角梁结构从初始屈曲到后屈曲并发生两态跳转过程中的位形曲线及非线性刚度.根据最小能量原理和挠曲线拐点个数,分析对称屈曲模态与非对称屈曲模态之间相互跳转的内在联系及其对结构非线性刚度突变的影响,得到了屈曲模态之间的转换条件.跳转过程的数值仿真表明,倾斜支撑梁结构发生大挠度后屈曲时具有明显的双稳态特性且只出现低阶(1、2阶)屈曲模态,仿真计算结果与试验结果相一致.     

Parametric instability of spinning twisted Timoshenko beams under compressive axial pulsating loads

The parametric instability on lateral bending vibrations of a spinning pretwisted beam under compressive axial pulsating forces is investigated. Equations of motion of the twisted beam are derived in the spinning twist coordinate frame using the Timoshenko beam theory and applying the Hamilton’s principle. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations with gyroscopic terms. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to obtain the boundary frequencies of instability regimes. The influence of twist angle, spinning speed, static component of axial force, aspect ratio and restraint condition on the instability regions of the spinning twisted Timoshenko beam is discussed.     

轴向力作用下连续梁固有振动分析

采用整体分析的方法,推导出轴向力作用下两端简支多跨均匀连续梁横向振动的频率方程和振型函数的解析式。所得公式包括了连续梁中间支座约束反力不全为零和全为零两种情形,对拉压轴向力、零轴向力和任意跨数均匀连续梁都适用。最后通过实例分析,说明了轴向力对连续梁固有频率的影响。     

弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解

基于Timoshenko梁理论研究弹性地基上转动功能梯度材料（FGM）梁的自由振动。首先确定功能梯度材料Timoshenko梁的物理中面,利用广义Hamilton原理推导出该梁在弹性地基上转动时横向自由振动的两个控制微分方程。其次采用微分变换法（DTM）对控制微分方程及其边界条件进行变换,计算了弹性地基上转动功能梯度材料Timoshenko梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种不同边界条件下横向自由振动的量纲一固有频率,与已有文献的计算结果进行比较,退化后结果一致。最后讨论了不同边界条件、转速、弹性地基模量和梯度指数对功能梯度材料Timoshenko梁自振频率的影响。结果表明：功能梯度材料Timoshenko梁的量纲一固有频率随量纲一转速和量纲一弹性地基模量的增大而增大;在量纲一转速和量纲一弹性地基模量一定的情况下,梁的量纲一固有频率随着功能梯度材料梯度指数的增大而减小。