Many Pulses Homoclinic Orbits and Chaotic Dynamics for Nonlinear Nonplanar Motion of a Cantilever Beam

The many pulses homoclinic orbits with a Melnikov method and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam are investigated in this paper for the first time. The cantilever beam studied here is subjected to a harmonic axial excitation and two transverse excitations at the free end. A generalized Melnikov method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of the cantilever beam. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. Numerical simulations are given to verify the analytical predictions. It is also found from the results of numerical simulation in three-dimensional phase space that the multi-pulse orbits exist for the nonlinear nonplanar oscillations of the cantilever beam.