Evaluating the response statistics of an uncertain bridge–vehicle system

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This paper addresses the statistical prediction of dynamic response of a bridge structure with inherent uncertainty under stochastic moving loads. The uncertainty in bridge structure, which is assumed with Gaussian properties, is modeled by the Spectral Stochastic Finite Element Method. The uncertain moving forces with Gaussian distribution are represented by the Karhunen–Loève expansion. The Polynomial chaos expansion is adopted to represent the uncertain response such that the proposed algorithm is not limited to system with small uncertainty. The bridge is modeled as a simply supported Bernoulli–Euler beam and the bridge–vehicle interaction forces are modeled as Gaussian random processes related to the power spectral density of the surface roughness defined in the ISO standard. The mathematical model of the bridge–vehicle system is formulated and solved with the Newmark-β method. The response statistics of the bridge are compared with those from Monte Carlo simulation. Different levels of uncertainty in both the system parameters and the moving forces are studied to investigate the accuracy and robustness of the proposed method in the stochastic analysis of the bridge–vehicle interaction problem.