Using the extended Melnikov method to study the multi-pulse global bifurcations and chaos of a cantilever beam

作者：Zhang W^*; Yao M H; Zhang J H

来源：Journal of Sound and Vibration, 2009, 319(1-2): 541-569.

DOI：10.1016/j.jsv.2008.06.015

The aim of this paper is to investigate the multi-pulse global bifurcations and chaotic dynamics for the nonlinear non-planar oscillations of a cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end by using an extended Melnikov method in the resonant case. First, the extended Melnikov method for studying the Shilnikov-type multi-pulse homoclinic orbits and chaos in high-dimensional nonlinear systems is briefly introduced in the theoretical frame. Then, this method is utilized to investigate the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics for the nonlinear non-planar oscillations of the cantilever beam. How to employ this method to analyze the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics of high-dimensional nonlinear systems in engineering applications is demonstrated through this example. Finally, the results of numerical simulation are given and also show that the Shilnikov-type multi-pulse chaotic motions can occur for the nonlinear non-planar oscillations of the cantilever beam, which verifies the analytical prediction.

• 出版日期2009-1-9
• 单位北京工业大学