Random vibration of systems with viscoelastic memory

The equation of motion of linear dynamic systems with viscoelastic memory is usually expressed in a integrodifferential form, and its numerical solution is computationally heavy. In two recent papers, the writers suggested that the system memory be accounted for through the introduction of a number of additional internal variables. Following this approach, the motion of the system is governed by a set of first-order, linear differential equations, whose solution is quite easy. In this paper, the approach is extended to single-degree-offreedom systems subjected to random, nonstationary excitation. The equations governing the time variation of the second-order statistics are derived, and an effective step-by-step solution procedure is proposed. Numerical example shows the accuracy of the procedure for white and nonwhite excitations.