Direct time-domain integration approach for viscoelastic systems involving various damping models

Abstract

Mechanical engineering systems with two or more parts of significantly different energy dissipation levels are encountered frequently in dynamical designs nowadays. Although dynamic analyses of only one exponential-like damping model in independent structures are studied by authors for decades, their counterpart for nonviscous systems involving various damping models seems not well-developed. In this paper, a time-domain analysis of various damping models subjected to arbitrary initial conditions is presented. The proposed approach is built on an extended state-space representation of the equations of motion. The method can be applied in both conditions when the damping matrices are of full rank or rank deficient in a uniform expression. The dynamic responses of the various damping models are calculated only by the original system matrices without solving the eigensolutions of the systems. This advantage particularly makes this method numerically efficient. Finally, a numerical example is offered to illustrate the accuracy of the derived method.