An inverse eigenvalue problem for damped gyroscopic second-order systems

Abstract

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):= λ 2 Ma +λ(D+G)+ Ka, where M a >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.