PARAMETER FREEZING PRECISE EXPONENTIAL INTEGRATOR AND ITS APPLICATION IN NONLINEAR VEHICLE-BRIDGE COUPLED VIBRATION

The basic problem describing vehicle-bridge interaction is a time-varying system problem, which the nonlinear characteristics need to be considered in many working conditions. It is difficult to get the analytical solution to this problem, and even the numerical solution may be complex. In this paper, focus on the solution to this problem, a parameter freezing precise exponential integrator is proposed and its application to vehicle-bridge coupled problem is analyzed. This algorithm combines the characteristics of precise integration and exponential integration, and freezes the parameters of time-varying coefficient matrix at each integration step to obtain the numerical solutions of vibration responses of the system. Considering the coupling relationship of the force and displacement between the vehicle tire and bridge deck, the asphalt pavement of the bridge deck, the viscoelastic and geometric nonlinear characteristics of the bridge, the vehicle-bridge coupled dynamic model is established. The parameter freezing precise exponential integrator is used to solve this dynamic model. By comparing with the approximate analytical solution, the solution calculated by the symplectic Runge-Kutta algorithm and the classical Newmark-β numerical integration method, the validity and accuracy of the proposed method are verified. On this basis, a scaled vehicle-bridge coupling system model is made. The mid-span deflection response is tested, which further verifies the validity and practicability of the theoretical model and proposed algorithm. The numerical characteristics of the proposed algorithm are analyzed by numerical calculation. Numerical results show that the proposed parameter freezing precise exponential integrator can not only deal with time-varying and nonlinear problems, but also has good numerical calculation accuracy and long-time numerical stability. Due to the characteristics of the precise integration, the time step can be set to be larger for the parameter freezing precise exponential integrator, which can effectively improve the calculation efficiency. Therefore, the proposed parameter freezing precise exponential integrator is expected to be a new and efficient algorithm for solving vehicle-bridge coupling dynamics problem.