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随机结构系统的一般实矩阵特征值问题的概率分析 总被引:9,自引:0,他引:9
由于工程实际结构的复杂性和所用材料在统计上的离散性以及测量、加工、制造误差的存在,必然导致具有随机参数的随机结构振动系统,按结构参数的性质来划分,随机振动问题包括两方面内容:(1)确定结构问题;(2)随机结构问题。本文以现代数学理论为依托,研究了随机结构系统的一般实矩阵的特征值问题。根据Kronecker代数、向量值和矩阵值函数的灵敏度分析、一般二阶矩法和概率摄动技术给出了计算随机结构系统的一般实矩阵的特征值和特征向量的数值方法,可以有效地得出随机结构系统的一般实矩阵的特征向量的统计量,发展了2D矩阵值函数的随机结构系统的特征值问题概率分析理论。 相似文献
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Chun Nam Wong Hong-Zhong Huang Jingqi Xiong Hua Long Lan 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(4):451-472
A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set
of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors
and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector
and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness
parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under
certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the
applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed.
In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient
for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile,
for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster
to the termination criterion. 相似文献
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Alexander P. Seyranian 《基于设计的结构力学与机械力学》2013,41(2):261-284
ABSTRACT This paper is devoted to sensitivity analysis of eigenvalues of nonsym-metric operators that depend on parameters. Special attention is given to the case of multiple eigenvalues. Due to the nondifferentiability (in the common sense) of multiple roots, directional derivatives of eigenvalues and eigenvectors in parametric space are obtained. Sensitivity analysis is based on the perturbation method of eigenvalues and eigenvectors. The generalized eigenvalue problem and vibrational systems are also investigated. Strong and weak interaction of eigenvalues are distinguished and interactions in two- and three-dimensional space are treated geometrically. It is shown that the strong interaction of eigenvalues is a typical catastrophe. Simple examples that illustrate the main ideas are presented. The results obtained are important for qualitative and quantitative study of mechanical systems subjected to static and dynamic instability phenomena. 相似文献
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A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system. 相似文献
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A new matrix perturbation analysis method is presented for efficient approximatesolution of the complex modal quadratic generalized eigenvalue problem of viscouslydamped linear vibration systems.First,the damping matrix is decomposed into the sum of aproportional-and a nonproportional-damping parts,and the solutions of the real modaleigenproblem with the proportional dampings are determined,which are a set of initialapproximate solutions of the complex modal eigenproblem.Second,by taking thenonproportional-damping part as a small modification to the proportional one and using thematrix perturbation analysis method,a set of approximate solutions of the complex modaleigenvalue problem can be obtained analytically.The result is quite simple.The new methodis applicable to the systems with viscous dampings-which do not deviate far away from theproportional-damping case.It is particularly important that the solution technique be alsoeffective to the systems with heavy,but not over,dampings.The solution formul 相似文献
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Every matrix is similar to a matrix in Jordan canonical form, which has very important sense in the theory of linear algebra and its engineering application. For a matrix with multiplex eigenvalues , an algorithm based on the singular value decomposition ( SVD ) for computing its eigenvectors and Jordan canonical form was proposed. Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues. It is superior to MATLAB and MATHEMAtICA. 相似文献
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齐朝晖 《应用数学和力学(英文版)》2002,23(2):187-193
IntroductionManymechanicalsystemscanbeviewedaslinearHamiltoniansystems.Whenwestudytheeffectsofsystemparametersonthebehaviorofthesystems,thesystemcanberegardedasthesystemdependingonparameters.Veryimportantsystemparameters ,suchascriticalload ,criticalang… 相似文献
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An acceleration for the eigensystem realization algorithm with partial singular values decomposition
The real-time identification of dynamic parameters is important for the control system of spacecraft. The eigensystem realization
algorithm (ERA) is currently the typical method for such application. In order to identify the dynamic parameter of spacecraft
rapidly and accurately, an accelerated ERA with a partial singular values decomposition (PSVD) algorithm is presented. In
the PSVD, the Hankel matrix is reduced to dual diagonal form first, and then transformed into a tridiagonal matrix. The eigenvalues
are computed by the bisection method in terms of the Sturm property, and the corresponding eigenvectors are obtained by the
inverse iteration method. Finally, the eigenvalues and the eigenvectors are transformed into the singular values and the singular
value vectors of the original matrix. An example for space station is presented to demonstrate the efficacy and accuracy of
the proposed algorithm. 相似文献
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边界约束刚度不确定的结构振动特征值 总被引:2,自引:0,他引:2
利用摄动法 ,将随机的微分方程和边界条件化为一系列的确定性微分方程和边界条件。运用有限元离散方法 ,推导了统计特征值的二阶摄动近似表达 ,用算例对本文方法进行了说明并和 Monte-Carlo模拟法结果进行了比较 相似文献
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目前在使用遗传算法或神经网络方法进行结构动力学损伤检测,需要基于少量的在线测量损伤结构数据和大量的数值仿真数据来实现,其中通过有限元方法来获得仿真数据的巨大计算量是动力学结构损伤检测方法发展中所面临的一个重要问题。本文在建模方面应用近年来提出的调整单元刚度模拟损伤的先进方法,以保证在损伤前后结构自由度数目不变;在此基础上应用特征值摄动法来减少损伤检测中计算量,并通过对复合材料层合板响应信号的小波分析验证了使用一阶矩阵摄动在有效降低计算量的同时,可以获得对损伤检测而言足够准确的响应信号。 相似文献
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《International Journal of Solids and Structures》2005,42(9-10):2883-2900
The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the complex eigenvalues of the non-proportional damping structures. By combining the interval mathematics and the finite element analysis, the mass matrix, the damping matrix and the stiffness matrix were represented as the interval matrices. Firstly, with the help of the optimization theory, we presented an exact solution—the vertex solution theorem, for determining the exact upper bounds or maximum values and exact lower bounds or minimum values of complex eigenvalues of structures, where the extreme values are reached on the boundary of the interval mass, damping and stiffness matrices. Then, an interval perturbation method was proposed, which needs less computational efforts. A numerical example of a seven degree-of-freedom spring-damping-mass system was used to illustrate the computational aspects of the presented vertex solution theorem and the interval perturbation method in comparison with Deif’s method. 相似文献
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把特征向量的各阶导数表示成所有模态的线性组合,并利用左模态与右模态间的双正交性,首先导出了任意非亏损矩阵的重特征值的一阶导数所满足的特征值问题,然后根据此特征值问题无、看重根的情况,再导出了异导重特征值和等导重特征值对应的可微特征向量、特征值和特征向量各阶导数的一般计算公式。算例显示了方法的正确性。 相似文献
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The perturbation method for the reanalysis of the singular value decomposition(SVD)of general real matrices is presented in this paper.This is a simple but efficientreanalysis technique for the SVD,which is of great worth to enhance computationalefficiency of the iterative analysis problems that require matrix singular valuedecomposition repeatedly.The asymptotic estimate formulas for the singular values and thecorresponding left and right singular vectors up to second-order perturbation componentsare derived.At the end of the paper the way to extend the perturbation method to the case ofgeneral complex matrices is advanced. 相似文献
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The criterion for the points in the parameter space being on the stability boundary of linear Hamiltonian system depending
on arbitrary numbers of parameters was given, through the sensitivity analysis of eigenvalues and eigenvectors. The results
show that multiple eigenvalues with Jordan chain take a very important role in the stability of Hamiltonian systems.
Foundation item: the National Natural Science Foundation of China (10072012); the National Natural Science Foundation of Russia
Biography: QI Zhao-hui (1964-) 相似文献
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This paper reports mathematical properties of the three-dimensional, first-order, velocity-stress equations for propagating
waves in anisotropic, linear elastic solids. The velocity-stress equations are useful for numerical solution. The original
equations include the equation of motion and the elasticity relation differentiated by time. The result is a set of nine,
first-order partial differential equations (PDEs) of which the velocity and stress components are the unknowns. Cast into
a vector-matrix form, the equations can be characterized by three Jacobian matrices. Hyperbolicity of the equations is formally
proved by analyzing (i) the spectrum of a linear combination of the three Jacobian matrices, and (ii) the eigenvector matrix
for diagonalizing the linearly combined Jacobian matrices. In the three-dimensional space, linearly combined Jacobian matrices
are shown to be connected to the classic Christoffel matrix, leading to a simpler derivation for the eigenvalues and eigenvectors.
The results in the present paper provide critical information for applying modern numerical methods, originally developed
for solving conservation laws, to elastodynamics. 相似文献
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本文利用子结构和Lanczos方法,提出了大型结构固有频率与模态的并行解法。该方法在Lanczos方法的求解过程中,仅利用子结构刚度阵和质量阵并行进行凝聚,进而求得新的迭代矢量,最终求得三对角阵对应的特征值和特征向量。该算法在西安交通大学ELXSI-6400并行计算机上程序实现,计算结果表明能有效地节省计算时间和计算机的内存,为一种有效的大型工程结构动力问题的求解方法。 相似文献