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

页码：685 / 707

页数：23

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