退化环面上的非线性jerk方程近似周期解的同伦分析方法  

Homotopy analysis method for approximate analytical periodic solutions of a nonlinear Jerk equation on a degenerate torus

作　　者：郑敏毅[1] 胡辉[1] 郭源君[1] 

机构地区：[1]湖南科技大学土木工程学院,湘潭411201

出　　处：《振动与冲击》2010年第5期46-49,77,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(50775071)

摘　　要：用同伦分析法求解退化环面上的非线性Jerk方程的近似周期和近似解析周期解。所得结果表明文中得到的一阶近似周期和一阶近似解析周期解与Gottlieb用低阶谐波平衡法求解得到的结果一样。当参数和初速度较大时,一阶近似周期与精确周期的百分比误差是4.831 8%,而二阶近似周期与精确周期的百分比误差小于0.219 9%。与数值方法给出的"精确"周期解比较,二阶近似解析周期解比一阶近似解析周期解要精确的多。因此,同伦分析法是求解非线性Jerk方程的一种非常有效的方法。Here,homotopy analysis method was applied to determine approximate periods and approximate analytical periodic solutions of a nonlinear Jerk equation on a degenerate torus.The results obtained revealed that the first-order approximate analytical periodic solution and the corresponding first-order approximate period are identical to those obtained via the first-order harmonic balance approach by Gottlieb;when the parameter and the initial velocity amplitude are larger,the percentage error of the first-order approximate period in relation to the exact one is 4.8318%,and the percentage error of the second-order approximate period in relation to the exact one is lower than 0.2199%;a comparison of the first and second analytical approximate periodic solutions with the numerically exact solutions shows that the second analytical approximate periodic solution is much more accurate than the first one;thus,homotopy analysis method is very effective for nonlinear Jerk equations.

关 键 词：非线性Jerk方程 近似周期解 谐波平衡法 摄动法 同伦分析法 

分 类 号：O322[理学—一般力学与力学基础]