Principal parametric resonances of non-linear mechanical system with two-frequency and self-excitations

被引：31
作者：
El-Bassiouny, AF [1 ]
机构：
[1] Benha Univ, Fac Sci, Dept Math, Banha, Egypt
来源：
MECHANICS RESEARCH COMMUNICATIONS | 2005年 / 32卷 / 03期
关键词：
non-linear system; parametric excitation; self-excitation; principal resonance; multiple scales method; stability;
D O I：
10.1016/j.mechrescom.2004.10.013
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
The principal parametric resonance of a single-degree-of-freedom system with non-linear two-frequency parametric and self-excitations is investigated. In particular, the case in which the parametric excitation terms with close frequencies is examined. The method of multiple scales is used to determine the equations that describe to first-order the modulation of the amplitude and phase. Qualitative analysis and asymptotic expansion techniques are employed to predict the existence of steady state responses. Stability is investigated. The effect of damping, magnitudes of non-linear excitation and self-excitation are analyzed. (c) 2004 Elsevier Ltd. All rights reserved.
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页码：337 / 350
页数：14
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