An inverse problem for undamped gyroscopic systems

作者：Yuan, Yongxin^*; Dai, Hua

来源：Journal of Computational and Applied Mathematics, 2012, 236(9): 2574-2581.

DOI：10.1016/j.cam.2011.12.015

• Inverse problem
• Gyroscopic system
• Complete prescribed spectral information
• Model updating
• Partial eigenstructure assignment

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.

• 出版日期2012-3
• 单位南京航空航天大学; 江苏科技大学