Narrow Results

In this paper, the midspan deflection of a beam bridge with vehicles passing through the bridge successively is investigated. The midspan deflection can be modeled as the vibration trace of smooth-and-discontinuous (SD) oscillator by considering the mode of the first order and up-and-down vibration. The nonlinear behaviors of the established model are studied and presented. KAM (Kolmogorov–Arnold–Moser) structures on the Poincaré section are constructed for the driven system without dissipation with generic KAM curve and a series of resonant points and the surrounding island chains connected by chaotic orbits. Introducing a series of complete elliptic integrals of the first and the second kind, the response curves of the system are detected, to which the effects of parameters are revealed. The relevant dynamics is depicted under external excitation exhibiting period leading to chaos. The efficiency of the bifurcation diagrams obtained in this paper is demonstrated via numerical simulations.