Spectral decomposition-based explicit integration method for fully non-stationary seismic responses of large-scale structures

Abstract

This paper presents a spectral decomposition-based explicit integration method for random vibration analysis of large-scale linear structures subjected to fully non-stationary seismic excitations. In this method, the seismic excitation process is decomposed using the spectral representation method, leading to a discrete representation of the excitation process in terms of an orthogonal random vector. Next, an explicit expression for the state response vector of structures with respect to the orthogonal random vector is derived by direct discretization and integration of the structural state equation, in which the time-dependent coefficient matrix can be obtained in a recursive manner. Since the state response vector contains only the displacement and velocity responses of structures, the finite-difference formulas are further used to obtain the explicit expression for the structural acceleration responses. These explicit expressions can be used not only to directly calculate the correlation matrix and evolutionary power spectral density of stochastic responses of structures, but also to efficiently evaluate the response samples required in the Monte Carlo simulation. For demonstration purposes, the proposed method is applied to the random vibration analysis of a coupled building system and a large-scale space-frame structure excited by two kinds of fully non-stationary seismic inputs; other existing methods are employed to illustrate the high accuracy and efficiency of the proposed method.