On the computation of frequency response matrices for systems in second-order form

Abstract

The purpose of this paper is to discuss the computation of the frequency response matrices of the form (P +jwR)(- w2M +jwG + K)-1B which are related to systems given in second-order form. For systems of this type, the above computational problem has not been considered in the literature so far. However, efficient and accurate computation of the frequency response matrices which are related to first-order models were recently presented and available where some of these methods depend mainly on the reduction of the state matrix to Hessenberg form using different means. On the other hand, the matrix form above has no Hessenberg analog and it is not so straightforward computationally. A simple partition to the matrix form is proposed so to allow a direct use to these methods. The use of the algorithms of these methods is introduced where their efficiency are compared using the operations count required. For accuracy comparison, we refer to some numerical examples.