An inverse problem for undamped gyroscopic systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Yuan, Yongxin¹  Dai, Hua² 

[1] Jiangsu Univ Sci & Technol, Sch Math & Phys, Zhenjiang 212003, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

关键词: Inverse problem;    Gyroscopic system;    Complete prescribed spectral information;    Model updating;    Partial eigenstructure assignment;   

DOI  :  10.1016/j.cam.2011.12.015

来源: Elsevier

【 摘 要 】

Linear undamped gyroscopic systems are defined by three real matrices, M > 0, K > 0, and G (G(T) = -G); the mass, stiffness, and gyroscopic matrices, respectively. In this paper an inverse problem is considered: given complete information about eigenvalues and eigenvectors, Lambda = diag{lambda(1), lambda(2), ... , lambda(2n-1), lambda(2n)} is an element of C-2nx2n and X = [x(1), x(2), ... , x(2n-1), x(2n)] is an element of C-nx2n, where the diagonal elements of Lambda are all purely imaginary, X is of full row rank n, and both Lambda and X are closed under complex conjugation in the sense that lambda(2j) = (lambda) over bar (2j-1) is an element of C, x(2j) = (x) over bar (2j-1) is an element of C-n for j = 1, ... , n, find M, K and G such that MX Lambda(2) + GX Lambda + KX = 0. The solvability condition for the inverse problem and a solution to the problem are presented, and the results of the inverse problem are applied to develop a method for model updating. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

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