Analytical analysis for large-amplitude oscillation of a rotational pendulum system

被引：18

作者：

Lai, S. K. ^{[1
]}

Lim, C. W. ^{[2
]}

Lin, Zhang ^{[1
]}

Zhang, W. ^{[3
]}

机构：

[1] City Univ Hong Kong, Bldg Energy & Environm Technol Res Unit, Div Bldg Sci & Technol, Hong Kong, Hong Kong, Peoples R China

[2] City Univ Hong Kong, Dept Bldg & Construct, Hong Kong, Hong Kong, Peoples R China

[3] Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 13期

基金：

中国国家自然科学基金;

关键词：

Chebyshev polynomials; Maclaurin series; Rotational pendulum system; Cubic-quintic Duffing equation; NONLINEAR OSCILLATIONS; VIBRATION ABSORBERS; BEAM; LINEARIZATION;

D O I：

10.1016/j.amc.2010.12.089

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：6115 / 6124

页数：10

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