Computational method of the non-stationary random responses for non-viscously damped structure systems

Non-viscous damping models in which the damping forces depend on the past history of velocities via convolution integrals over some kernel functions have risen in many different subjects. The aim of this paper is to develop a computational method of the non-stationary random responses for the non-viscously damped structure systems subjected to the nonstationary random excitations. The formulas of the non-stationary response of the nonviscously damped structure systems are derived, based on the pseudo excitation method, discrete convolution algorithm and Newmark method. A computational procedure for the nonstationary random response of the non-viscously damped structure systems is given in detail. Finally, the non-stationary response analyses of two frames with non-viscous dampers, subjected to uniformly modulated evolutionary random seismic excitation, are studied to elucidate the proposed method.