An Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

Abstract EN

The inverse eigenvalue problem of constructing symmetric positive semidefinite matrix D (written as D≥0) 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, Ka≥0 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.