非线性振动系统同(异)宿分岔问题的研究  

Study about homoclinic and heteroclinic orbit bifurcation problems of nonlinear vibration systems

作　　者：张春友[1] 陈雪艳[1] 

机构地区：[1]内蒙古民族大学机械工程学院,内蒙古通辽028000

出　　处：《辽宁工程技术大学学报（自然科学版）》2015年第8期979-982,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金项目(6144041)

摘　　要：为解决传统方法在求解非线性振动系统同(异)宿分岔问题过于复杂的问题,以双曲函数摄动法为基础,通过解析非线性振动系统派生方程,再对得出的解析解进行摄动得到最终解析式,提出了计算非线性振动系统同(异)宿轨道解析式更加有效的方法,简化了现有方法求解的复杂性.The linear theory has played an important role in the development of human engineering technology, but many dynamic questions in reality are nonlinear. While the homoclinic （heteroclinic） orbit is seen as the boundary between periodic and non-periodic motion that nonlinear vibration systems take. Also it is the core content of studying global bifurcation problems of nonlinear vibration systems. Based on hyperbolic function perturbation method, the paper obtains the final analytic perturbation by analyzing the derived equations of the nonlinear vibration systems and then carrying the perturbation of the analytical solution. According to all above, the paper proposes a more effective way to calculate the analytical expression about homoclinic（heteroclinic） orbit in nonlinear vibration systems, which simplifies the complexity of the conventional solving method.

关 键 词：非线性系统 分岔 同(异)宿轨道 双曲函数摄动法 解析式 

分 类 号：TH113.1[机械工程—机械设计及理论]