An exact and efficient time-domain method for random vibration analysis of linear structures subjected to uniformly modulated or fully non-stationary excitations

This paper presents a novel time-domain method for non-stationary random vibration analysis of linear structures. Specifically, using the well-known spectral representation method, the stochastic excitation process is first decomposed into a set of trigonometric basis functions (TBFs) modulated by a series of orthogonal basis random variables (BRVs). Next, each TBF is used as a deterministic excitation input for the structural model, and the induced structural responses are derived analytically using the modal superposition method. After superposition of each TBF-induced deterministic responses, an explicit closed-form expression between the structural stochastic responses and the BRVs is derived, based on which the response statistics of structures at any time instant can be evaluated easily. Furthermore, the accuracy of the solution is independent of the time step used. Finally, several numerical examples in civil engineering, including a Euler beam under stochastic moving load and a shear frame structure subjected to uniformly modulated or fully non-stationary seismic motions, are studied to illustrate the performance of the proposed method. The obtained structural response statistics are compared with the solutions obtained by the Monte Carlo and evolutionary spectral methods. The results verified the high accuracy and efficiency of the proposed method.