Direct time-domain integration method for exponentially damped linear systems

Time-domain analysis of multiple-degree-of-freedom linear non-viscously damped systems is considered. It is assumed that the non-viscous damping forces depend on the past history of velocities via convolution integrals over exponentially decaying kernel functions. A direct time-domain integration method is proposed. The proposed approach is based on an extended state-space representation of the equations of motion. The state-space method, in turn, is based on introduction of a set of internal variables. The numerical method for the calculation of the displacements eliminates the need for explicit calculation of the velocities and usually large number of internal variables at each time step. This fact particularly makes this method numerically efficient. The proposed method is illustrated by two numerical examples.