A semi-analytical method in bridge-vehicle dynamic interaction and its field study

Abstract

The vehicle bridge interaction typically represents dynamics of an oscillator moving on flexible beam. In this paper, a flexible oscillator and beam coupled dynamics has been outlined in presence of random excitation using Monte Carlo simulation with analytically derived samples. The random excitation is imposed on the moving oscillator due to unevenness present on the surface of the beam and has been represented by power spectral density function. The surface unevenness is considered as superposition of Gaussian random process with variable deterministic surface which renders it a non-homogeneous random process in space. Formulation is done in state-space form with complex modal decomposition of dynamic system equations. In the process, it has been shown that the response integral can be transformed to the integration of simple analytical functions consisting of modulated waves of randomly varying phase angles and amplitudes. This enables one to evaluate the integrals in closed-form using symbolic packages and interface to the computer program for faster generation of samples. The entire process of Monte Carlo simulation has been illustrated with the data of a simply supported bridge and vehicle. Results of the proposed method have been validated with numerical solution and experimental result available in the literature. Field test has been conducted and a comparative study of model behavior has been made with the field results and Finite Element Analysis using CSI Bridge. The proposed method can avoid numerical integration required to generate large number of samples in Monte Carlo Simulation and can save overall computational time, while quite accurately predicting the response.