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摘要:
The multipulse Shilnikov orbits and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam are studied 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. The nonlinear governing equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equations to obtain a two-degree-of-freedom nonlinear system under combined parametric and forcing excitations. The resonant case considered here is principal parametric resonance-1/2 subharmonic resonance for the first mode and fundamental parametric resonance-primary resonance for the second mode. The parametrically and externally excited system is transformed to the averaged equation by using the method of multiple scales. From the averaged equation, the theory of normal form is used to find their explicit formulas. Based on normal form obtained above, the dissipative version of the energy-phase method is utilized to analyze the multipulse global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of the cantilever beam. The energy-phase method is further improved to ensure the equivalence of topological structure for the phase portraits. The analysis of global dynamics indicates that there exist, the multipulse jumping orbits in the perturbed phase space of the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the multipulse Shilnikov type chaotic motions can occur for the nonlinear nonplanar oscillations of the cantilever beam. 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 multipulse Shilnikov type orbits exist for the nonlinear nonplanar oscillations of the cantilever beam.
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通讯作者信息:
来源 :
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN: 0218-1274
年份: 2005
期: 12
卷: 15
页码: 3923-3952
2 . 2 0 0
JCR@2022
ESI学科: MATHEMATICS;
JCR分区:2