Slow passage through resonance in Mathieu's equation

Leslie Ng; Richard Rand; Michael O'Neil

doi:10.1177/1077546303009006004

Slow passage through resonance in Mathieu's equation

Leslie Ng, Richard Rand, Michael O'Neil

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 equations to obtain an analytic approximation.

Original language	English (US)
Pages (from-to)	685-707
Number of pages	23
Journal	JVC/Journal of Vibration and Control
Volume	9
Issue number	6
DOIs	https://doi.org/10.1177/1077546303009006004
State	Published - Jun 2003

Keywords

Amplification
Mathieu equation
Parametric excitation
Resonance

ASJC Scopus subject areas

Automotive Engineering
General Materials Science
Aerospace Engineering
Mechanics of Materials
Mechanical Engineering

Access to Document

10.1177/1077546303009006004

Cite this

@article{5ca46b30c5bc43d892289305cdb6ea1f,

title = "Slow passage through resonance in Mathieu's equation",

abstract = "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 equations to obtain an analytic approximation.",

keywords = "Amplification, Mathieu equation, Parametric excitation, Resonance",

author = "Leslie Ng and Richard Rand and Michael O'Neil",

year = "2003",

month = jun,

doi = "10.1177/1077546303009006004",

language = "English (US)",

volume = "9",

pages = "685--707",

journal = "JVC/Journal of Vibration and Control",

issn = "1077-5463",

publisher = "SAGE Publications Inc.",

number = "6",

}

TY - JOUR

T1 - Slow passage through resonance in Mathieu's equation

AU - Ng, Leslie

AU - Rand, Richard

AU - O'Neil, Michael

PY - 2003/6

Y1 - 2003/6

N2 - 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 equations to obtain an analytic approximation.

AB - 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 equations to obtain an analytic approximation.

KW - Amplification

KW - Mathieu equation

KW - Parametric excitation

KW - Resonance

UR - http://www.scopus.com/inward/record.url?scp=0037596766&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037596766&partnerID=8YFLogxK

U2 - 10.1177/1077546303009006004

DO - 10.1177/1077546303009006004

M3 - Article

AN - SCOPUS:0037596766

SN - 1077-5463

VL - 9

SP - 685

EP - 707

JO - JVC/Journal of Vibration and Control

JF - JVC/Journal of Vibration and Control

IS - 6

ER -

Slow passage through resonance in Mathieu's equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this