Stability Analysis of Mathieu Equation by Floquet Theory and Perturbation Method

摘要: ABSTRACT In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from linear natural frequencies. The Mathieu equation sim-plest differential with periodic coefficients, which lead to excitation. may have unbounded solutions. This work conducted stability analysis for equation, using Floquet theory and numerical method. Using Lindstedt’s perturbation method, harmonic solutions transition curves separating stable un-stable motions were obtained. unstable re-gions calculated. method had same as Increased regions due inclusion damping * 1. 서 론 일정한 계수를 가진 운동방정식의 외부 가진은 그 주파수가 선형 고유진동수가 일치할 때만 큰 응답을 주지만, 주기적으로 변하는 운동방정식에서 매개 가진(parametric excitation)은 고유진동수와 멀리 떨어져 있을 때도 응답이 발생한다