双铰抛物线弹性拱的混沌行为

In order to design an arch structure with good nonlinear dynamic characteristics, the nonlinear dynamic behaviors under a long time external force have to be investigated. The chaotic behaviors of the parabolic elastic arch with two hinge supports subjected to a transverse distributed varying periodic excitation are investigated in this paper. Based on the geometric equation of deformable body and the equilibrium equations of an arch element, the nonlinear dynamic model which dominates the transverse vibration of the elastic arch is established first,and then the nonlinear differential dynamic system is obtained by using Galerkin’s method, thus the fixed points and the homoclinic orbits are found out. The critical condition of chaotic vibration of the elastic arch is obtained through the Melnikov's method. Finally the dynamic characteristics (such as Lyapunov exponents and Lyapunov dimension and the phase trajectories and also the Poincare map etc.) which can be used to explain the dynamic behaviors of the differential dynamic system of the elastic arch are calculated by using numerical simulation for different parameters. It is found that the motion of the parabolic elastic arch with two hinge supports subjected to a transverse periodic excitation may be stationary or chaotic motion. The stationary motion occurs if the amplitude of the transverse periodic excitation is small, but the chaotic motion occurs if the amplitude is large.