Nonstationary random vibration analysis of fractionally-damped systems by numerical explicit time-domain method

Abstract

Random vibration analysis of fractionally-damped systems has received considerable attentions over the past two decades. In this paper, an efficient explicit time-domain approach is developed to determine the response statistics of multi-degrees-of-freedom linear systems endowed with fractional derivative terms subjected to nonstationary random excitations. The explicit time-domain expression of the state vector is constructed for the fractionally-damped system, and on this basis, the statistical moments of responses are directly formulated with the moment operation rule or efficiently calculated with the Monte-Carlo simulation. Dimension-reduced statistical analysis can be easily conducted just focusing on certain responses of interest with the use of the explicit expressions of dynamic responses. The present approach can account for nonstationary random excitations with arbitrary evolutionary power spectrum forms, even of the non-separable kind. A 20-degrees-of-freedom shear-type fractionally-damped system subjected to fully nonstationary random excitation is analysed to illustrate the accuracy and efficiency of the proposed method.