Nonlinear dynamic analysis of a parametrically excited vehicle–bridge interaction system

In this paper, a nonlinear supported Euler–Bernoulli beam under harmonic excitation coupled to a 2 degree of freedom vehicle model with cubic nonlinear stiffness and damping is investigated. The equations of motion are derived by Newton’s law and discretized into a set of coupled second-order nonlinear differential equations via Galerkin’s method with cubic nonlinear terms. Based on the created model, numerical simulations have been conducted using the Runge–Kutta integration method to perform a parametric study on influences of the nonlinear support stiffness coefficient, mass ratio, excitation amplitude and position relation for the vehicle–bridge interaction (VBI) system by using bifurcation diagram and 3-D frequency spectrum. The results indicate that depending on different parameters, a diverse range of periodic motion, quasi-periodic response, chaotic behavior and jump discontinuous phenomenon are observed. And the chaotic regions are scattered between a number of periodic/quasi-periodic motions. The study may contribute to a further understanding of the dynamic characteristics and present useful information to dynamic design and vibration control for the VBI system.