轴向激励屈曲简支梁动力特性的数值研究

Numerical Investigation on Dynamical Behaviours of A Buckled Beam Under Axial Harmonic Excitation

利用有限差分原理 ,考虑转动惯量的影响 ,在轴向激励作用下 ,对屈曲梁的动力特性进行数值研究。用数值方法进行计算的结果与利用Galerkiin法将偏微分方程转化成常微分方程进行分析的结果基本吻合 ,证实系统中存在周期倍化、拟周期运动和混沌运动等复杂动力学行为 。

The dynamical behaviours of a simply support buckled beam under axial harmonic excitation are investigated using the direct numerical method,and the effect of rotary inertia is considered too.The governed equation of buckled beam is transformed to the nonlinear partial differential equations of physical variables such as moment,velocity and displacement.By using a stable,explicit finite difference scheme to solve the equations and the solutions is equivalent to the Galerkiin solutions.Various complex dynamical behaviours such as period doubling,quasi periodic and chaotic motion in this system are shown,and the result also demonstrated that the finite difference method is more convenient than other tradition methods for the study of buckled beams.