A direct-variance-analysis method for generalized stochastic eigenvalue problem based on matrix perturbation theory  

作　　者：QIU ZhiPing QIU HeChen 

机构地区：[1]Institute of Solid Mechanics,Beihang University

出　　处：《Science China(Technological Sciences)》2014年第6期1238-1248,共11页中国科学（技术科学英文版）

基　　金：supported by the AVIC Research Project(Grant No.cxy2012BH07);the National Natural Science Foundation of China(Grant Nos.10872017,90816024,10876100);the Defense Industrial Technology Development Program(Grant Nos.A2120110001,B2120110011,A082013-2001);"111" Project(Grant No.B07009)

摘　　要：It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more rigorous.Therefore the uncertainty effects are indispensable during the process of product development.Besides,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best design.Taking uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational costs.Owing to the situations above,matrix perturbation method has been investigated by researchers worldwide recently.However,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational process.This has become the bottleneck of application for matrix perturbation method.In this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation method.In the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have changed.Combining the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure directly.Hence the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being involved.The feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing structure of MA700 commercial aircraft),in which the D

关 键 词：matrix perturbation theory generalized stochastic eigenvalue problem structure with random parameter direct variance analysis 

分 类 号：O327[理学—一般力学与力学基础] O342[理学—力学]