二自由度碰振准哈密顿系统双碰周期解的Melnikov方法  

Melnikov′s Method of Periodic Solutions with Double Impacts for a 2-DOF Vibro-impact Quasi-Hamiltonian System

作　　者：张思进[1] 刘喻 吉德三[2] ZHANG Sijin;LIU Yu;JI Desan(College of Mechanical and Vehicle Engineering, Hunan University,Changsha 410082,China;College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]湖南大学机械与运载工程学院,湖南长沙410082 [2]武汉科技大学理学院,湖北武汉430065

出　　处：《湖南大学学报（自然科学版）》2019年第2期67-74,共8页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(11372101)~~

摘　　要：采用摄动法和Poincaré映射方法推导出了具有立方非线性项和外部激励项的二自由度碰振系统周期解的扩展Melnikov函数,并运用该Melnikov函数研究了二自由度碰振系统的双碰周期解特性,确定了系统稳定双碰周期2运动的存在条件,即在参数域内的一条临界曲线.通过数值模拟验证,结果表明:该临界曲线下方区域参数是双碰周期2运动,上方区域参数是非双碰周期2运动;当保持其他参数不变,仅增加系统激励幅值f时,系统的运动状态会从多碰多周期运动逐步向双碰周期2运动转变;当保持其他参数不变,仅增加系统恢复系数η0时,系统的运动状态会从双碰周期2运动逐步向多碰多周期运动转变.Perturbation method and Poincaré mapping method were used to derive the generalized Melnikov function of the periodic solution for a two-degree-of-freedom vibro-impact system with cubic non-linearity and external excitations. By using the Melnikov′s method, the characteristics of periodic motions with double-impact of the 2-dof system were studied, and the existence condition of period-2 motions with double-impact was determined as a critical curve in the parameter domain. The results of numerical simulations show that the regions below the critical curve are the period-2 motions with double-impact, the upper regions of the critical curve are not period-2 motions with double-impact;Meanwhile,increasing the force amplitude and keeping the other parameters unchanged, the motion state of the system changes from multi-period motions with multi-impact to period-2 motions with double-impact, while increasing the system restitution coefficient and keeping the other parameters unchanged, the motion state of the system changes from period-2 motions with double-impact to multi-period motions with multi-impact.

关 键 词：碰振系统 MELNIKOV方法 双碰周期2运动 POINCARÉ映射 扩展Melnikov函数 

分 类 号：O322[理学—一般力学与力学基础]