Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.