Frequency analysis of strongly nonlinear generalized Duffing oscillators using He's frequency-amplitude formulation and He's energy balance method

被引：121

作者：

Younesian, Davood ^{[1
]}

Askari, Hassan ^{[1
]}

Saadatnia, Zia ^{[1
]}

KalamiYazdi, Mohammad ^{[2
]}

机构：

[1] Iran Univ Sci & Technol, Sch Railway Engn, Tehran 16846, Iran

[2] Iran Univ Sci & Technol, Dept Mech Engn, Tehran 16846, Iran

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 09期

关键词：

Nonlinear vibration; Generalized Duffing equation; He's frequency-amplitude formulation; He's energy balance method; HOMOTOPY PERTURBATION METHOD;

D O I：

10.1016/j.camwa.2010.03.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, He's Frequency-Amplitude Formulation (HFAF) and He's Energy Balance Method (HEBM) are employed to solve the generalized Duffing equation in the form of <(x)double over dot> + x + a(3)x(3) + a(5)x(5) + alpha(7)x(7) + ... + alpha(n)x(n) = 0. For any arbitrary power of n, a frequency analysis is carried out and the relationship between the natural frequency and the initial amplitude is obtained in analytical form. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on the HFAF, HEBM and exact integration method. Numerical simulations are extended for even very strong nonlinearities and very good correlations are achieved between the numerical results. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：3222 / 3228

页数：7

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