碰振准哈密顿系统局部亚谐轨道的Melnikov方法  

The Melnikov′s method for local-subharmonic orbits of a vibro-impact quasi-Hamiltonian system

作　　者：张思进[1] 文桂林[1] 王紧业 徐慧东[1] 

机构地区：[1]湖南大学机械与运载工程学院,湖南长沙410082

出　　处：《振动工程学报》2016年第2期214-219,共6页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(11372101;11225212和11002052)

摘　　要：将Melnikov方法应用于碰振准哈密顿系统的局部亚谐轨道,推导出了局部亚谐轨道的Melnikov函数。该函数可以用于确定存在局部亚谐轨道及极限环分岔的条件。给出的局部亚谐轨道Melnikov函数和同宿轨道Melnikov函数共同揭示了准哈密顿系统的诸多动力学特征;然后,通过数值方法模拟受迫碰振振子运动,验证了局部亚谐Melnikov函数的正确性。The Melnikovfs method is applied on a vibro-impact quasi-Hamiltonian system, and a Melnikov function for local- subharmonic orbits is derived. The function can be applied to determine the existence of local-subharmonic orbits, as well as the conditions of limit cycle bifurcations. The so-called local subharmonic Melnikov function, together with the one for homoclinic orbit, reveals lots of dynamical features of the quasi-Hamiltonian system. The local-subharmonic Melnikov function is validated by numerical simulations of a forced vibro-impact oscillator.

关 键 词：MELNIKOV方法 局部亚谐轨道 碰振准哈密顿系统 同宿轨道 POINCARÉ映射 

分 类 号：O322[理学—一般力学与力学基础]