Approximate Random Vibration Analysis of Classically Damped MDOF Systems

Abstract

A new approximate asymptotic method is presented for the nonstationary response of classically damped MDOF (multidegree‐of‐freedom) linear systems to a general class of nonstationary stochastic excitations. The method is based on a simplification of the equations for the modal covariance response by neglecting secondary dynamical effects in the modal Liapunov equation. A comprehensive study is presented which provides general conditions involving the system and excitation characteristics for which the approximations are reliable. The proposed technique reliably predicts the essential features of the statistics of MDOF response for a broad range of system and excitation parameters, and provides valuable insight into the nonstationary response characteristics. Certain similarities and differences between the nonstationary and stationary response are revealed. The method is applicable to both lightly and heavily damped systems, and to various types of nonwhite excitations, 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.