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multi-pulse homoclinic orbits and chaotic dynamics of a parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities

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Science China(Physics,Mechanics & Astronomy) 2014年第6期57卷 1098-1110页

作者： ZHANG Wei HUANG YuTong YAO MingHui College of Mechanical Engineering Beijing University of Technology

In this paper,the complicated dynamics and multi-pulse homoclinic orbits of a two-degree-of-freedom parametrically excited nonlinear nano-oscillator with coupled cubic nonlinearities are *** damping,parametrical excitation and the nonlinearities are regarded as *** averaged equation depicting the fast and slow dynamics is derived through the method of multiple *** dynamics near the resonance band is revealed by doing a singular perturbation analysis and combining the extended Melnikov *** are able to determine the criterion for the existence of the multi-pulse homoclinic orbits which can form the Shilnikov orbits and give rise to *** last,numerical results are also given to illustrate the nonlinear behaviors and chaotic motions in the nonlinear nano-oscillator.

关键词： nonlinear nano-oscillator extended Melnikov method multi-pulse homoclinic orbit chaotic dynamics

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multi-pulse orbitS AND CHAOTIC DYNAMICS OF A COMPOSITE LAMINATED RECTANGULAR PLATE

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Acta Mechanica Solida Sinica 2011年第5期24卷 383-398页

作者： Xiangying Gu Wei Zhang Minghui Yao College of Mechanical Engineering Beijing University of Technology Beijing 100124 China

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy＇s third-order shear deformation plate theory and the model of the yon Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton＇s principle. Then, using the second-order Galerkin dis- cretization, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1：1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The theoretic results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation, which also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

关键词： composite laminated plate third-order shear theory multi-pulse homoclinic orbit chaos

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