### 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 travelling through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The WKB method is then applied to the slow flow equations to get an analytic approximation.

Original language | English (US) |
---|---|

Title of host publication | Design Engineering |

Publisher | American Society of Mechanical Engineers (ASME) |

Pages | 131-140 |

Number of pages | 10 |

ISBN (Print) | 0791836282, 9780791836286 |

State | Published - 2002 |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Design Engineering*(pp. 131-140). American Society of Mechanical Engineers (ASME).

**Slow passage through resonance in mathieu's equation.** / Ng, Leslie; Rand, Richard; O'Neil, Michael.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Design Engineering.*American Society of Mechanical Engineers (ASME), pp. 131-140.

}

TY - GEN

T1 - Slow passage through resonance in mathieu's equation

AU - Ng, Leslie

AU - Rand, Richard

AU - O'Neil, Michael

PY - 2002

Y1 - 2002

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 travelling through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The WKB method is then applied to the slow flow equations to get 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 travelling through the tongue and the initial conditions. We use the method of multiple scales to obtain a slow flow approximation. The WKB method is then applied to the slow flow equations to get an analytic approximation.

UR - http://www.scopus.com/inward/record.url?scp=78249283574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78249283574&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:78249283574

SN - 0791836282

SN - 9780791836286

SP - 131

EP - 140

BT - Design Engineering

PB - American Society of Mechanical Engineers (ASME)

ER -