A Direct Eigenanalysis of Multibody System in Equilibrium
Joint Authors
Yang, Cheng
Cao, Dazhi
Zhao, Zhihua
Zhang, Zhengru
Ren, Gexue
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-16
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
This paper presents a direct eigenanalysis procedure for multibody system in equilibrium.
The first kind Lagrange’s equation of the dynamics of multibody system is a set of differential algebraic equations, and the equations can be used to solve the equilibrium of the system.
The vibration of the system about the equilibrium can be described by the linearization of the governing equation with the generalized coordinates and the multipliers as the perturbed variables.
But the multiplier variables and the generalize coordinates are not in the same dimension.
As a result, the system matrices in the perturbed vibration equations are badly conditioned, and a direct application of the mature eigensolvers does not guarantee a correct solution to the corresponding eigenvalue problem.
This paper discusses the condition number of the problem and proposes a method for preconditioning the system matrices, then the corresponding eigenvalue problem of the multibody system about equilibrium can be smoothly solved with standard eigensolver such as ARPACK.
In addition, a necessary frequency shift technology is also presented in the paper.
The importance of matrix conditioning and the effectiveness of the presented method for preconditioning are demonstrated with numerical examples.
American Psychological Association (APA)
Yang, Cheng& Cao, Dazhi& Zhao, Zhihua& Zhang, Zhengru& Ren, Gexue. 2012. A Direct Eigenanalysis of Multibody System in Equilibrium. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-993443
Modern Language Association (MLA)
Yang, Cheng…[et al.]. A Direct Eigenanalysis of Multibody System in Equilibrium. Journal of Applied Mathematics No. 2012 (2012), pp.1-12.
https://search.emarefa.net/detail/BIM-993443
American Medical Association (AMA)
Yang, Cheng& Cao, Dazhi& Zhao, Zhihua& Zhang, Zhengru& Ren, Gexue. A Direct Eigenanalysis of Multibody System in Equilibrium. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-12.
https://search.emarefa.net/detail/BIM-993443
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993443