Abstract:A pseudo-steady state method for analyzing random responses of coupled vehicle-track systems subjected to track irregularities is developed. The vehicle is simplified as a three dimensional multi-rigid body dynamic system and the track is modeled by the generalized finite element method. Assume that the sleeper spans are uniform, and then the equation of motion of the coupled system is periodically time-varying. Pseudo-excitation method (PEM) is used to transform the three types of rail irregularities into harmonic pseudo-excitations; the differential equations theory and the Schur decomposition scheme are then applied to develop a pseudo-steady state method for solving the above equation of motion. In this method, a linear equation set with an upper triangular coefficient matrix is established to replace the conventional step-by-step integration process when calculating the pseudo-responses of PEM which considerably reduces the computational effort. The random response of a three-dimensional coupled vehicle-track system is analyzed in the numerical example and the transmission mechanism of random vibration in the coupled system is investigated.