非线性自治振动系统同宿解的广义双曲函数摄动法  

Generalized Hyperbolic Perturbation Method for Homoclinic Solutions of Strongly Nonlinear Autonomous Systems

作　　者：陈洋洋[1] 燕乐纬[2] 佘锦炎[3] 陈树辉[4] 

机构地区：[1]广州大学,减震控制与结构安全教育部重点实验室,广州510405 [2]广州大学工程力学系,广州510405 [3]香港大学机械工程系,中国香港 [4]中山大学应用力学与工程系,广州510405

出　　处：《应用数学和力学》2012年第9期1064-1077,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10972240),国家自然科学青年基金资助项目(11102045);广东省自然科学博士启动基金资助项目(S2011040004039);广东省高校优秀青年创新人才培育基金资助项目(LYM10108);广州市高校科研基金资助项目(10A024);香港研究资助局研究基金资助项目(GRF HKU 7173 09E)

摘　　要：提出广义的双曲函数摄动法,用于求解强非线性自治振子的同宿解,克服一般摄动步骤中派生方程须存在显式精确同宿解的限制.以广义双曲函数作为摄动步骤的基本函数,拓展了基于双曲函数的摄动法的适用范围.对同时含2,3次和含4次强非线性项的系统进行求解分析,验证了方法的有效性和精度.A generalized hyperbolic perturbation method was presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure was improved for those systems whose exact homoclinic generating solutions could not be explicitly derived.The generalized hyperbolic functions were employed as the basis functions in the present procedure to extend the validity of the hyperbolic perturbation method.Several strongly nonlinear oscillators with quadratic,cubic and quartic nonlinearity were studied in details to illustrate the efficiency and accuracy of the present method.

关 键 词：广义双曲函数摄动法 自激系统 同宿解 

分 类 号：O322[理学—一般力学与力学基础]