Abstract
The multipulse homoclinic orbits and chaotic dynamics of a reinforced composite plate with the carbon nanotubes (CNTs) under combined in-plane and transverse excitations are studied in the case of 1 : 1 internal resonance. The method of multiple scales is adopted to derive the averaged equations. From the averaged equations, the normal form theory is applied to reduce the equations to a simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. The energy-phase method proposed by Haller and Wiggins is utilized to examine the global bifurcations and chaotic dynamics of the CNT-reinforced composite plate. The analytical results demonstrate that the multipulse Shilnikov-type homoclinic orbits and chaotic motions exist in the system. Homoclinic trees are constructed to illustrate the repeated bifurcations of multipulse solutions. In order to verify the theoretical results, numerical simulations are given to show the multipulse Shilnikov-type chaotic motions in the CNT-reinforced composite plate. The results obtained here imply that the motion is chaotic in the sense of the Smale horseshoes for the CNT-reinforced composite plate.
Highlights
Carbon nanotubes (CNTs), as a new type of advanced materials, have attracted a lot of attention of researchers.is is because CNTs possess high strength and stiffness with high aspect ratio and low density
Zhu et al [2] presented the bending and free vibration analysis of CNT-reinforced composite plates using the finite element method based on the first-order shear deformation plate theory
Wang and Shen [3] examined the nonlinear dynamic response of CNT-reinforced composite plates resting on elastic foundations in thermal environments. e motion equations were derived based on a higher-order shear deformation theory with a von Karmantype of kinematic nonlinearity
Summary
Carbon nanotubes (CNTs), as a new type of advanced materials, have attracted a lot of attention of researchers. Zhu et al [2] presented the bending and free vibration analysis of CNT-reinforced composite plates using the finite element method based on the first-order shear deformation plate theory. In order to eliminate or suppress large nonlinear vibrations and chaotic motions of the CNTreinforced composite plate, we should deepen and complete the theoretical analysis on the CNT-reinforced composite plate model, discuss the complex dynamic behaviors, explore the existence conditions of the multipulse Shilnikov-type orbits, and analyze the impact of parameters on the system, so as to ensure the stability and controllability of the CNT-reinforced composite plate. E energy-phase method developed by Haller and Wiggins [20] is applied to study the multipulse homoclinic bifurcations and chaotic dynamics for the CNT-reinforced composite plate.
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