A Numerical Method for Solving Evolutionary Statistical Characteristics of Dynamic Responses of the Vehicle–Bridge Coupled System Based on the Recursion Principle

The vehicle–bridge coupled (VBC) vibration problem under the excitation of road roughness is essentially a nonstationary random vibration problem. At present, the computational efficiency is still the key factor of restricting the application of the stochastic vibration theory in nonlinear dynamic systems. In this study, the covariance between the system excitation and response is used to recursively solve the variance of the system response, and an efficient numerical method of solving the evolutionary statistical moments of dynamic responses of the time-variant VBC system is proposed. The study shows that the results obtained by the recursion method are consistent with the explicit time-domain method, and are further verified by the Monte Carlo method. Furthermore, the method proposed is applied to study the impact factor spectrum of highway beam bridges. The deficiency of the existing impact factor spectrum formula is pointed out, and an effective method is put forward.