Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model

A new method of dynamic analysis on the bridge–vehicle interaction problem considering uncertainties is proposed in this paper. The bridge is modeled as a simply supported Euler–Bernoulli beam with Gaussian random elastic modulus and mass density of material with moving forces on top. These forces are time varying with a coefficient of variation at each time instance and they are considered as Gaussian random processes. The mathematical model of the bridge–vehicle system is established based on the finite element model in which the Gaussian random processes are represented by the Karhunen–Loéve expansion and the equations will be solved by the Newmark  -ββ method. The proposed method is compared with the Monte Carlo method in numerical simulations with good agreements for cases with different vehicle speed and level of uncertainties in the excitation and system parameters. The mean value and variance of the structural responses are found to be very accurate even with large uncertainties in the excitation forces. The proposed method is also found to have superior performance in the computational efficiency compared with the Monte Carlo method.