Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Stability Analysis of Mathieu Equation by Floquet Theory and Perturbation Method

Floquet 이론과 섭동법에 의한 Mathieu Equation의 안정성해석

  • Park, Chan Il (Department of Precision Mehanical Engineering, Gangneung-Wonju National University)
  • Received : 2013.05.15
  • Accepted : 2013.07.18
  • Published : 2013.08.20
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Abstract

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

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References

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