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

Content Provider	Springer Nature Link
Author	Qiu, ZhiPing Qiu, HeChen
Copyright Year	2014
Abstract	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-Variance-Analysis (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 truss-system and the other is wing structure of MA700 commercial aircraft), in which the DVA method also shows superiority in computational efficiency when compared to the Monte-Carlo method.
Starting Page	1238
Ending Page	1248
Page Count	11
File Format	PDF
ISSN	16747321
Journal	Science in China Series E: Technological Sciences
Volume Number	57
Issue Number	6
e-ISSN	18691900
Language	English
Publisher	Science China Press
Publisher Date	2014-05-13
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	matrix perturbation theory generalized stochastic eigenvalue problem structure with random parameter direct variance analysis Engineering
Content Type	Text
Resource Type	Article
Subject	Engineering Materials Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Eigenvalue problems of rotor system with uncertain parameters

Stochastic perturbation theory (1988).

Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures

A meshfree method for computational stochastic mechanics (2001)

Unified calculation of eigen-solutions in power systems based on matrix perturbation theory

Random eigenvalue problems revisited

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

Perturbation analysis for the eigenvalue problem of a formal product of matrices

Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices (2000)

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

Similar Documents

Eigenvalue problems of rotor system with uncertain parameters

Stochastic perturbation theory (1988).

Perturbation Finite Element Transfer Matrix Method for Random Eigenvalue Problems of Uncertain Structures

A meshfree method for computational stochastic mechanics (2001)

Unified calculation of eigen-solutions in power systems based on matrix perturbation theory

Random eigenvalue problems revisited

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

Perturbation analysis for the eigenvalue problem of a formal product of matrices

Perturbation Analysis for the Eigenvalue Problem of a Formal Product of Matrices (2000)

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