摘要
基于碳纳米管增强复合材料板结构的非线性动力学方程,利用多尺度法得到该系统在1:3内共振情况下的平均方程.运用规范型理论对平均方程化简,研究了化简后系统未受扰部分的非线性动力学行为和扰动项对系统流形的影响.同时,利用能量-相位法验证了系统存在多脉冲跳跃轨线,进而证明在一定参数条件下碳纳米管增强复合材料板结构中存在Smale马蹄意义下的混沌.所得结论具有重要理论价值,对实际工程具有指导意义.
Based on the nonlinear governing equation of the carbon nanotube-reinforced composite plate,the averaged equation under 1∶ 3 internal resonances is obtained by using the method of multiple scales. It is then simplified by means of the normal form theory. The nonlinear dynamics of the unperturbed system and the effect of the perturbation terms on the manifold are investigated. Energy-phase method is used to validate the existence of the multi-pulse jumping orbits. It is eventually to approved that chaotic dynamics in the sense of Smale horseshoes takes place at the carbon nanotube-reinforced composite plate under certain parameters. The results also provides essential data for theoretical analysis and engineering practice.
出处
《动力学与控制学报》
2016年第2期109-114,共6页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(11290152)~~
关键词
碳纳米管
复合材料板
能量相位法
多脉冲
混沌
carbon nanotube
composite material plate
energy-phase method
multi-pulse orbit
chaotic motion
