Direct convolution integration method for random vibration analysis of structures subjected to nonuniformly modulated nonstationary excitations

• An efficient computational method is presented for nonstationary random vibration analysis of structures. • The equal initial condition method is used to identify structural unit impulse response. • Two fast Fourier transform algorithms are used to accelerate the convolution integration. • Three schemes are established and compared in the practical application. A comprehensive direct convolution integration method is presented in this study for the random vibration analysis of linear structures subjected to multiple nonuniformly modulated nonstationary excitations. The structural unit impulse responses with respect to each independent excitation are first identified and stored by a few time-history analyses. Then the structural response statistics are calculated by the direct convolution integration of unit impulse responses and excitation statistics. Further, two fast Fourier transform algorithms are presented to speed up the convolution integration. Because the convolution expressions are explicit, the presented method can be used to only calculate the responses at some specific degrees of freedom of interest in engineering. Furthermore, it can only calculate the responses at a small number of sparse moments in consideration of the time slow-varying property of nonstationary processes. Finally, the random vibration analysis of a frame structure excited by the fully coherent and incoherent nonstationary excitations is utilized to demonstrate its high accuracy and efficiency. Some suggestions of application are given.