Semi-analytical solution of vehicle–bridge interaction on transient jump of wheel

A semi-analytical method of vehicle–bridge interactions is presented in this paper, and the separation between vehicle and bridge is discussed. The interaction of the two subsystems is implemented by a Hertz contact spring. With this new method, the mass and damping matrices in system equations are given as not time-dependent and semi-analytical solution of the simply-supported bridge model with moving vehicles (as sprung masses) is obtained, where a kind of different coupling stiffness matrix is used. The numerical example demonstrates that when there is no jump of the wheel, the result from the new method is consistent to the traditional one. When the jump happens, the new method also yields a true result, while the traditional cannot. Considering random and abrupt irregularity on bridges, the transient jump of vehicles is also discussed in this paper and the results show the efficiency of the presented method.