An inverse problem for undamped gyroscopic systems

摘要

Linear undamped gyroscopic systems are defined by three real matrices, M>0,K>0, and G(GT=−G); the mass, stiffness, and gyroscopic matrices, respectively. In this paper an inverse problem is considered: given complete information about eigenvalues and eigenvectors, Λ=diag{λ1,λ2,…,λ2n−1,λ2n}∈C2n×2n and X=[x1,x2,…,x2n−1,x2n]∈Cn×2n, where the diagonal elements of Λ are all purely imaginary, X is of full row rank n, and both Λ and X are closed under complex conjugation in the sense that λ2j=λ̄2j−1∈C,x2j=x̄2j−1∈Cn for j=1,…,n, find M,K and G such that MXΛ2+GXΛ+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.