Slow passage through resonance in Mathieu's equation

被引：12
|
作者：
Ng, L [1 ]
Rand, R [1 ]
O'Neil, M [1 ]
机构：
[1] Cornell Univ, Dept Theoret & Appl Mech, Ithaca, NY 14853 USA
来源：
JOURNAL OF VIBRATION AND CONTROL | 2003年 / 9卷 / 06期
关键词：
resonance; Mathieu equation; amplification; parametric excitation;
D O I：
10.1177/107754603029581
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
We investigate slow passage through the 2:1 resonance tongue in Mathieu's equation. Using numerical integration, we find that amplification or de-amplification can occur. The amount of amplification (or de-amplification) depends on the speed of travel through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The Wentzel-Kramers-Brillouin (WKB) method is then applied to the slow flow equations to obtain an analytic approximation.
引用
收藏
页码：685 / 707
页数：23
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