A direct approach to second-order matrix non-classical vibrating equations

Abstract

A direct framework is developed for secoud-order matrix equations without transforming it into a first-order companion equatiou. lt is done in terms of its matrix impulse response that is directly related to the t ransfer matrix. Wc formulate an extension of the Cayley-Hamilton identity, derive t he controllability and observabili ty matrices and discuss Krylov's method in terms of such matrix response. This formulation will allow to furth er discuss Arnoldi and Lanczos methods as well as time-integratiou by FFT 2