On the efficacy and accuracy of freezing technique for the response analysis of time-varying vehicle-bridge interaction systems

Abstract The basic problem of vehicle-bridge interaction (VBI) is a linear time-varying system for which no exact solution is available and even numerical solutions can be complicated. In this paper, the efficacy and accuracy of a freezing technique (FT), in which the time parameter is frozen, applied to obtain the forced response of the VBI system are assessed. To improve the accuracy, a time-step approach, in which FT is employed in each time subinterval, is proposed. The FT is relatively simple to implement and results are validated with and compared to those obtained by a highly accurate Runge-Kutta method (treated as “exact” solution) for different vehicle models, vehicle and bridge parameters, and time steps. It is found that numerical results obtained by the FT are accurate, even for high vehicle speeds. Moreover, the FT outperforms the Newmark-β method. An analytical local error bound for the FT is derived, which shows the error dependence on the vehicle-bridge coupling dynamics, in particular, the tire stiffness and the vehicle speed. An important implication of this study is that, since the FT can be applied to analyze the time-varying VBI system, the method essentially transforms the coupled system into a time sequence of linear time-invariant (LTI) systems and allows tools for dynamic analysis and controller design of LTI systems to be applicable to the VBI problem.