Approximate analytical solutions for oscillatory and rotational motion of a parametric pendulum

被引：102
|
作者：
Xu, Xu [1 ]
Wiercigroch, M. [1 ]
机构：
[1] Univ Aberdeen, Dept Engn, Ctr Appl Dynam Res, Aberdeen AB24 3UE, Scotland
来源：
NONLINEAR DYNAMICS | 2007年 / 47卷 / 1-3期
关键词：
parametric pendulum; nonlinear dynamical system; perturbation method; oscillations; rotations;
D O I：
10.1007/s11071-006-9074-4
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this paper, the authors have studied dynamic responses of a parametric pendulum by means of analytical methods. The fundamental resonance structure was determined by looking at the undamped case. The two typical responses, oscillations and rotations, were investigated by applying perturbation methods. The primary resonance boundaries for oscillations and pure rotations were computed, and the approximate analytical solutions for small oscillations and period-one rotations were obtained. The solution for the rotations has been derived for the first time. Comparisons between the analytical and numerical results show good agreements.
引用
收藏
页码：311 / 320
页数：10
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