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http://dx.doi.org/10.5050/KSNVE.2013.23.8.734

Stability Analysis of Mathieu Equation by Floquet Theory and Perturbation Method  

Park, Chan Il (Department of Precision Mehanical Engineering, Gangneung-Wonju National University)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.23, no.8, 2013 , pp. 734-741 More about this Journal
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.
Keywords
Stability; Mathieu Equation; Floquet Theory; Perturbation Method;
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Times Cited By KSCI : 1  (Citation Analysis)
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