Inverse Eigenvalue Problem with Non-simple Eigenvalues for Damped Vibration Systems

In this paper, we will present a general form of real and symmetric n x n matrices M, C and K for a quadratic inverse eigenvalue problem QIEP: Q(lambda) Xi ( lambda M-2 + lambda C + K) x = 0, so that Q(lambda) has a prescribed set of k eigenvalues with algebraic multiplicity ni, i = 1, ... , k ( which 2n(1) + 2n(2) + ... + 2n(l) +n1=1+1 + ... + nk = 2n). This paper generalizes the method of inverse problem for selfadjoint linear pencils, to self- adjoint quadratic pencils Q(lambda). It is shown that this inverse problem involves certain free parameters. Via appropriate choice of free variables in the general form of QIEP, we solve a QIEP.