Semi‐analytical solutions for stochastic response of non‐classically damped linear structures to arbitrary time‐frequency modulated seismic excitations

Abstract

AbstractThis paper presents a semi‐analytical method for stochastic response analysis of non‐classically damped linear structures subjected to non‐stationary seismic excitations modeled by arbitrary time‐frequency modulating functions. In this method, the inherent randomness of seismic excitation process is characterized by a set of orthogonal random variables obtained using the spectral representation method. Then, by adopting piecewise polynomials to interpolate the time‐frequency modulating function of seismic excitation, an explicit expression for the structural stochastic response in term of the orthogonal random variables is derived using the complex modal analysis. This expression can be used not only to efficiently predict the seismic response of structures subjected to an arbitrary excitation sample, but also to directly evaluate the structural response statistics in the time domain. Finally, a robust algorithm is proposed to determine the optimal locations of segmentation points for the piecewise polynomials, the computational efficiency can be further improved. In the numerical application, a typical non‐classically damped structural system subjected to two models of non‐stationary seismic excitations are studied. The classical evolutionary spectral method and the Monte Carlo simulation are used to verify the accuracy and efficiency of the proposed method. The effects of several parameters such as the order of polynomials on the performance of the proposed method are investigated.