A stochastic analysis method of transient responses using harmonic wavelets, part 2: Time-dependent vehicle-bridge systems

Abstract Conventional stochastic response analysis methods of vehicle-bridge (VB) systems involve a brute-force calculation based on a large number of simulations, which imposes huge computational burdens because the dynamic analysis of a time-dependent VB system requires repeated assembles of system matrices. This paper proposes a novel stochastic analysis method of transient responses for time-dependent VB systems based on periodic generalized harmonic wavelets (GHW). We establish the equations of motion of the VB system and reveal the orthogonal characteristic relationships between the time-dependent system matrices and the wavelet functions. Then, two sets of linear algebraic equations of wavelet coefficients are established for describing the time-dependent VB system, and the time-varying power spectral density functions of system responses are obtained in a semi-analytical form. The stochastic response analysis of the time-dependent VB system is therefore converted into solving a set of linear algebraic equations, which significantly simplifies the stochastic response analysis. The accuracy and efficiency of the proposed method are validated via comparison against the Monte Carlo simulations of nonstationary stochastic analyses of a highway bridge and a railway bridge, respectively. The proposed method provides a high-efficient way to estimate the time-varying power spectral density functions of stochastic responses of time-dependent VB systems.