APPROXIMATE RANDOM VIBRATION ANALYSIS OF CLASSICALLY DAMPED MDOF SYSTEMS

A new approximate asymptotic method is presented for the nonstationary response of classically damped MDOF (multidegree-of-freedom) linear s ystems to a general class of nonstationary stochastic excitations. The method is based on a simplification of the equations for the modal co variance response by neglecting secondary dynamical effects in the mod al Liapunov equation. A comprehensive study is presented which provide s general conditions involving the system and excitation characteristi cs for which the approximations are reliable. The proposed technique r eliably predicts the essential features of the statistics of MDOF resp onse for a broad range of system and excitation parameters, and provid es valuable insight into the nonstationary response characteristics. C ertain similarities and differences between the nonstationary and stat ionary response are revealed. The method is applicable to both lightly and heavily damped systems, and to various types of nonwhite excitati ons, including excitation processes with slowly varying intensity and frequency content encountered in earthquake engineering applications. The performance of the new method is demonstrated by some examples.