Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 725616, 10 pages
Research Article

An Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

School of Mathematics and Physics, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Received 31 March 2009; Accepted 29 August 2009

Academic Editor: Jerzy Warminski

Copyright © 2009 Yongxin Yuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The inverse eigenvalue problem of constructing symmetric positive semidefinite matrix D (written as D0) and real-valued skew-symmetric matrix G (i.e., GT=G) of order n for the quadratic pencil Q(λ):=λ2Ma+λ(D+G)+Ka, where Ma>0, Ka0 are given analytical mass and stiffness matrices, so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are specified.