轴向激励屈曲简支梁混沌运动特性

Chaotic Behavior of a Simply-supported Buckled Beam Under Axial Harmonic Excitation

文章利用有限差分原理对轴向激励作用下屈曲梁的动力特性进行数值研究,并考虑了梁转动惯量的影响。其计算结果与利用Galerkiin法将偏微分方程转化成常微分方程进行分析研究结果基本吻合,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,结果也表明该方法具有良好的精确性和收敛性。

The dynamical behavior of a simply-support buckled beam under axial harmonic exci-tation is investigated by using the direct numerical method and the effect of rotary inertia is con-sidered,too.The governed equation of buckled beam is transformed to the nonlinear partial differ-ential equations of physical variables such as moment ,velocity and displacement.By using a sta-ble,explicit finite difference scheme to solve the equations,the solutions are equivalent to the Galerkin solutions.Various complex dynamical behavior such as period doubling,quasi-periodic and chaotic motion in this system are shown,and the result also demonstrates that the finite dif-ference method is more convenient than other tradition methods to study buckled beam.