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薄膜横向振动的有限元分析

ISSN号：1000-4939
期刊名称：应用力学学报
时间：0
页码：44-49+109
分类：O175.25[理学—数学;理学—基础数学] Q141[生物学—生态学;生物学—普通生物学]
作者机构：[1]Key Laboratory of Vibration Control and Structural Safety of Ministry of Education of China, Guangzhou University, Guangzhou 510405, P. R. China, [2]Department of Engineering Mechanics, Guangzhou University, Guangzhou 510405, P. R. China, [3]Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China, [4]Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China
相关基金：Project supported by the National Natural Science Foundation of China （Nos. 10972240 and 11102045）, the Natural Science Foundation of Guangdong Province of China （No. S20110400040）, the Foundation of Guangdong Education Department of China （No. LYM10108）, the Foundation of Guangzhou Education Bureau of China （No. 10A024）, and the Research Grant Council of Hong Kong of China （No. GRF-HKU-7173-09E）
相关项目：非线性振动系统双曲函数方法及其应用研究

关键词：非线性自治系统, 双曲线函数, 摄动方法, 广义, 强非线性振动, 扰动方法, 多项式, 振荡器, generalized hyperbolic perturbation method, nonlinear autonomous system, homoclinic solution

中文摘要：

A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators,in which the perturbation procedure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived.The generalized hyperbolic functions are 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 are studied in detail to illustrate the efficiency and accuracy of the present method.

英文摘要：

A generalized hyperbolic perturbation method is presented for homoclinic solutions of strongly nonlinear autonomous oscillators, in which the perturbation proce- dure is improved for those systems whose exact homoclinic generating solutions cannot be explicitly derived. The generalized hyperbolic functions are 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 are studied in detail to illustrate the efficiency and accuracy of the present method.

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