Complex Modal Analysis for Generally Viscous and Visco-elastic Damped Vibratory System

Abstract

We examined a complex modal analysis of generally viscous and visco-elastic damped vibratory system, which include viscous damping proportional to the velocity of the masses and viscoelastic damping proportional to the force of the linear springs. In this paper, we propose to express the symmetrical state-space equations of the target system in Co-Hamiltonian form to apply the complex modal analysis. We performed numerical simulations for a 3 DOF (Degree of Freedom) system with viscoelastic damping and showed that the state-space equations can be decoupled by the proposed method. We also confirmed that the inverse identification of the forces proposed by the authors for generally viscous damped vibratory system reconstructed the multiple different excitation forces with reasonable accuracy.