• 한국소음진동공학회논문집
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• 제23권8호
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• pp.734-741
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• 2013

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.

• 대한기계학회논문집A
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• 제29권10호
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• pp.1321-1328
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• 2005

Based upon the Floquet theory, the complex modal solution for general rotor systems with periodically time-varying parameters is newly derived. The complete modal response can be obtained from the orthonormality condition between the time-variant eigenvectors and the corresponding adjoint vectors. The harmonic solutions such as the response and directional special a patterns are then derived in terms of harmonic modes whose coefficients are obtained from the modal analysis. The stability analysis by the Floquet's transition matrix and the eigen-analysis is also performed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.877-882
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• 2005

Dynamic stability of an axially accelerating beam stucture is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively targe unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• 소음진동
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• 제9권6호
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• pp.1157-1165
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• 1999

Dynamic stability of a flying structure undertaking constnat and pulsating thrust force is investigated in this paper. The equations of motion of the structure, which is idealized as a free-free beam, are derived by using the hybrid variable method and the assumed mode method. The structural system includes a directional control unit to obtain the directional stability. Unstable regions due to periodically pulsating thrust forces are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the constant force, the location of gimbal, and the frequency of pulsating force. The validity of the diagrams are confirmed by direct numerical simulations of the dynamic system.

• 한국소음진동공학회논문집
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• 제15권9호
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• pp.1053-1059
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• 2005

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• 대한전자공학회논문지SD
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• 제40권4호
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• pp.27-33
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• 2003

최근, 원통형 DFB전송 구조들은 다양한 광 소자들과 결합하여 광통신용 필터로 널리 사용되고 있다. 이 원통형 Bragg 격자 구조들의 광 필터특성을 분석하기 위하여 본 논문에서는 Floquet-Babinet의 원리에 의존한 새롭고 쉬운 모드 전송선로 이론 (Modal Transmission-Line Theory)을 제시하였다. 수치해석 결과, 제안한 해석법은 원통형 DFB전송 구조들의 필터특성을 분석하기 위한 유용한 프로그래밍 알고리즘을 제공하고, 다층 원통형 주기 구조들의 전송특성을 분석하기 위하여 쉽게 발전시킬 수 있음을 보였다.

• 소음진동
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• 제9권2호
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• pp.355-362
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• 1999

Vibration reduction of an optical disk drive is achieved by an automatic ball balancer and dynamic behaviors of the drive are studied by theoretical approaches. Using Lagrange's equation, we derive nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of equilibrium positions, the Floquet theory is applied to the perturbed equations. On the other hand, time responses are computed by an explicit time integration method. We also investigate the effects of mass center and the position of the ABB on the dynamic behaviors of the system.

• Kyungpook Mathematical Journal
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• 제30권1호
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• pp.21-28
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• 1990

• 한국광학회지
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• 제17권3호
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• pp.209-215
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• 2006

협대역 천이영역을 갖는 원통형 격자전송구조 (Circular Bragg Grating: CBG) 가 최근 DWDM을 위한 광통신용 대역통과 필터로 널리 사용되고 있다. 이 원통형 Bragg 격자 구조들의 광 필터특성을 분석하기 위하여 본 논문에서는 Floquet-Babinet의 원리에 의존하는 새로운 해석적인 모드 전송선로 이른 (Modal Transmission-Line Theory: MTLT)을 제시하였다. 수치해석 결과, 제안한 해석법은 CBG의 필터특성을 분석하기 위한 유용한 프로그래밍 알고리즘을 제공하고, 다층 원통형 주기 구조들의 그 전송특성을 분석하기 위하여 쉽게 발전시킬 수 있음을 보였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2005년도 창립60주년 기념 추계 학술대회
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• pp.185.1-185.1
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• 2005