柔性悬臂梁非线性非平面运动的多脉冲轨道分析

MULTI-PULSE ORBITS IN NONLINEAR NON-PLANAR MOTION OF A CANTILEVER BEAM

首先建立了柔性悬臂梁非线性非平面运动的偏微分方程;然后运用Galerkin和多尺度方法得到平均方程。并利用规范形理论进一步将方程化简;最后用能量相位法求出多脉冲跳跃的能量函数序列,Dynamics软件数值计算表明:在系统中确实存在着由多脉冲跳跃而导致的Smale马蹄型混沌.

First we formulated a set of integral-partial differential governing equations,which describes the non-linear non-planar oscillations of a cantilever beam. Then by applying the Galerkin procedure and the multi-scale method, we obtained the averaged equations; From the partial differential governing equations and from the averaged equation and by using the theory of normal form,we found the explicit formulas of normal form. Based on the normal form obtained above, the dissipative version of the energy-phrase method was utilized to analyze the multi-pulse global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam,which predicted that there are some multi-pulse Shilnikov type orbits. The numerical simulations shows that the multi-pulse Shilnikov type orbits do exist in the nonlinear nonplanar oscillations of the cantilever beam.