重频结构大修改动力重分析的矩阵摄动法

为拓展矩阵摄动法在结构重分析中的适用范围,提高重分析计算精度,针对重频结构参数大修改提出了重频结构动力重分析的矩阵摄动法。采用高次增量法将反映重频结构参数改变的质量矩阵和刚度矩阵的增量分别表示为小参数ε的一次与二次幂项之和,根据矩阵摄动理论推导得到重特征值的二阶摄动解及相应特征向量的一阶摄动解。数值算例表明,所提出方法极大提高了重频结构大修改下的动力重分析计算精度。     

基于摄动传递矩阵法的随机参数系统振动分析

随机参数对多刚柔体结构动态特性具有一定影响,含随机参数系统的振动特性分析是现代多刚柔体结构研制与动态性能设计的重要环节之一。基于多体系统传递矩阵法和摄动方法,推导了含随机参数系统零阶、一阶和二阶摄动总传递方程,建立了含随机参数的多体系统特征值问题的分析方法,实现了含随机参数柔性结构振动特性快速分析。分别应用文中方法与Monte Carlo方法对某含随机参数的柔性结构和平面振动多刚柔体系统特征值问题进行了分析,两种方法的计算结果吻合较好,证明了文中方法的有效性和高效性。     

动力响应问题的摄动Riccati传递矩阵方法

基于Riccati传递矩阵法,给出了一维不确定参数结构系统动力学响应问题的二阶摄动计算方法。该方法在用于一维结构系统动力响应问题的摄动分析时,不需要按振型展开,避免了基于有限元的矩阵摄动方法所带来的模态截断误差问题,提高了分析结果的精度。以多跨转子——轴承系统为模型,导出了动力响应问题摄动R iccati传递矩阵法的具体计算公式,并编制了相应的计算分析程序。算例对弹性支承的等截面梁的动力响应问题进行了摄动分析,摄动计算结果和精确计算结果吻合良好。     

动力响应问题的一阶摄动传递矩阵法

基于Riccati传递矩阵法，给出了一维不确定参数结构系统动力响应问题的一阶摄动计算方法。该方法在用于求解一维结构系统动力响应问题时，不需要按振型展开，因此，可以避免基于有限元法的矩阵摄动所带来的模态截断误差问题，从而提高分析结果的精度。算例对简支梁和锅炉给水泵转子的动力响应问题进行了一阶摄动分析；当ε较小时，一阶摄动计算结果和精确计算结果吻合良好。     

一维随机参数结构的特征值问题

基于摄动传递矩阵的理论，给出一维随机参数结构系统特征值和特征向量的计算分析方法。用一个具有随机质量密度和截面直径的简支梁的理论结果，验证文中方法的正确性。     

锅炉给水泵转子动力学参数的二阶摄动识别

利用摄动传递矩阵法,结合实验室的试验,对某电站锅炉给水泵转子的动力学参数进行了一阶和二阶摄动识别。给出了给水泵转子上的热装叶轮、轴套对转子刚度产生加强作用的一、二阶摄动识别结果．得到了修正的给水泵转子系统动力学计算模型。由修正模型计算得到的转子系统固有频率与实测的转子系统固有频率吻合良好。指出一阶摄动识别的结果可以满足工程实际的精度要求。     

振动系统特征值问题的矩阵灵敏度分析

应用Kronecker代数和矩阵微分理论，系统地发展了振动系统的特征值和特征向量的矩阵灵敏度分析方法，给出了向量值和矩阵值数的结构系统的特征值和特征向量的灵敏度，通过求导数排列成二维矩阵，所得的结果易形成计算机程序。该方法可以扩展延伸到具有一般矩阵和重根的特征值灵敏度分析的问题之中。     

摄动法在局部结构动力修改逆问题中的应用研究

提出了用摄动法求解实模态情况下局部结构动力修改逆问题的方法 ,推导了质量修改和刚度修改的摄动公式并给出了求解方法 ,可直接求得结构质量参数或刚度参数的修改量。与一阶摄动法相比 ,二阶摄动法可用于修改量较大的情况。     

基于BFGS摄动法的固定梁损伤检测

运用损伤结构的特征值问题,建立拟牛顿法的BFGS优化摄动方法来检测固定梁的损伤情况。多单元两端固定梁的损伤位置与程度,可以从首几对振动模态在数次迭代內准確获取。首先,摄动展开损伤结构的刚度矩阵、特征值和特征向量,并代入损伤结构的特征值方程;然后,集合p阶的弹性模量摄动项,以显式直接推导特征参数的p阶摄动系数;最后,把系数代入摄动方程,对于多个弹性模量进行BFGS拟牛顿优化迭代,其目标函数由摄动方程剩余项的总和产生。使用两端固定梁的有限元模型,五单元至九单元梁的损伤检测验证了该方法在有限模态参数与减少自由度模型的有效性。在终止准则方面,使用了d-模与t-模比较不同迭代阶段的收敛性,并精确地在0.06~0.001弹性模量误差內检测了小至大损伤的各个单元号及其损伤程度。     

客运架空索道系统动力特性分析方法

客运架空索道系统的固有频率与模态是衡量索道系统固有动力特性的重要指标，固有频率的大小直接关系到结构在各种不同的激励条件下是否会发生动力放大效应与共振。文中首先解决索道系统分析中的有限元建模问题，包括典型柔性索道的模型状态，然后利用ANSYS程序的子空间迭代法求出结构最低各阶的特征值与特征向量，并计算出三种工况下的前40阶固有频率与振动模态，为客运架空索道系统的动力特性分析提供有效的计算方法。     

Eigenvalue problems of rotor system with uncertain parameters

A general method for investigating the eigenvalue problems of a rotor system with uncertain parameters is presented in this paper. The recurrence perturbation formulas based on the Riccati transfer matrix method are derived and used for calculating the first- and secondorder perturbations of eigenvalues and their respective eigenvectors for the rotor system with uncertain parameters. In addition, these formulas can be used for investigating the independent, and repeated, as well as the complex eigenvalue problems. The general method is called the Riccati perturbation transfer matrix method (Riccati-PTMM). The formulas for calculating the mean value, variance, and covariance of the eigenvalues and eigenvectors of the rotor system with random parameters are also given. Riccati-PTMM is used for calculating the random eigenvalues of a simply supported Timoshenko beam and a test rotor supported by two oil bearings. The results show that the method is accurate and efficient.     

大型机械动力学设计的复模态矩阵摄动法

针对现有的大型机械动力学设计的复模态矩阵摄动法不能简单地唯一确定特征向量的所有摄动系数这一缺陷,作者在文［１］中通过引进一个简单的范化条件,导出了孤立复特征值情况的复模态矩阵摄动公式。但该法对系统存在重特征值时失效。为此,本文进一步研究了重特征值的复模态矩阵摄动法,详细导出了相应的摄动公式。     

结构动力修改的循环对称摄动新方法

利用结构的循环对称特性，以矩阵摄动理论和复约束法、伪单元法为基础，提出结构动力修改的循环对称摄动新方法，通过对循环对称扇区模型的分析获得整个循环对称结构特征值和特征向量的变化，大规模减少了这类结构动力修改的计算工作量，大大提高了计算效率。算例证明方法正确、有效、简捷。     

Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant “no spill-over property” of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show that the proposed method considerably reduces both feedback norms and the sensitivity of the closed-loop eigenvalues. A study on robustness of the system responses of the method under small perturbations show that the responses of the perturbed closed-loop system are compatible with perturbations.     

随机参数结构系统特征对的随机性及其关系分析

以随机参数结构系统为对象,分析并揭示了结构特征值与特征向量二者随机性之间的关系。利用瑞利商公式分析了结构特征值的随机性;利用结构动力特征方程分析了特征值与特征向量随机性之间的联系;从正则振型的表达式出发,导出了结构正则振型的随机性表达式。通过十杆桁架和三盘两轴扭转系统两个算例考察了结构各个参数的随机性对特征对随机性的影响,通过与MonteCarlo数值模拟法结果比较,验证了理论分析和计算方法的正确性。     

应用根轨迹分析阻尼器对机械结构系统特征值的影响

对于由粘性阻尼器控制的机械结构系统，利用该系统的复特征值对阻尼系数的导数及根轨迹曲线研究了结构系统复特征值的分布规律。该研究对于确定阻尼器的安置位置及阻尼系数有一定参考价值。     

MODAL MODIFICATION OF VIBRATING SYSTEMS: SOME PROBLEMS AND THEIR SOLUTIONS

Experimental modal testing data form an incomplete set of natural frequencies and mode shapes. The incompleteness of modal representation is inherent also to continuous systems that are represented by discrete models. Furthermore, current state-of-the-art numerical methods for determining the eigenvalues of large discrete systems can extract only some eigenvalues and eigenvectors associated either with low frequencies or the high-frequency range. Therefore, when predicting the effect of structural modification on the spectrum of a modified structure an error called a ‘truncation error’ exists in the calculations.The paper focuses on the prediction of the error in the spectrum of a modified structure resulting from the incomplete representation of the model. An optimal solution in a Rayleigh–Ritz sense is derived and the truncation error is bounded. Then the inverse problem of determining the structural modification that is needed to assign the spectrum is considered. A mathematical formulation characterising a continuous family of solutions is first given. Then a procedure for determining physical realisable solutions is developed. Finally, it is shown that if both left and right eigenvectors of the system are known then it is possible to solve the inverse structural modification problem without truncation error. The extraction of left eigenvectors from experimental data, however, can be an ill-conditioned problem. Thus, the modification could be sensitive to noise in the measured data, and the truncation error alone might not be the dominant mechanism of error.