• 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.

• 전기전자학회논문지
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• 제17권4호
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• pp.559-563
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• 2013

본 논문에서는 ISF와 Floquet 벡터에 각각 기초하는 두 개의 주요한 발진기 위상잡음 이론의 등가성을 해석적으로 증명한다. 이를 위해 본 연구에서는 ISF에 기초하는 위상잡음 이론으로부터 전력 스펙트럼 밀도 행렬을 구한다. 이렇게 함으로써 ISF에 기초한 위상잡음 이론의 전력 스펙트럼 밀도 행렬과 Floquet 벡터에 기초한 위상잡음 이론의 전력 스펙트럼 밀도 행렬이 같다는 사실을 해석적으로 증명할 수 있으며 이는 두 이론이 본질적으로 등가임을 증명한다. 본 연구의 목적은 현재까지 널리 알려진 상기 두 위상잡음 이론사이의 관계에 대한 보다 깊은 통찰력을 제공하는데 있다.

• Ocean Systems Engineering
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• 제4권3호
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• pp.243-261
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• 2014

Aqua is an underwater biomimetic vehicle designed and built at McGill University that uses six paddles to produce control and propulsion forces. It has the particularity of having time-periodic thrust due to its oscillating paddles. Using an existing model of the vehicle, two types of controller were developed: a PD controller and a Floquet controller. The Floquet controller has the advantage of explicitly addressing the time-periodicity of the system. The performance of the controllers was assessed through simulation and experimentally in the Caribbean Sea. We find that the vehicle was able to follow the prescribed trajectories with relative accuracy using both controllers, though, the Floquet controller slightly outperforms the PD controller. Furthermore, a key advantage of the Floquet controller is that it requires no tuning while the PD controller had to be tuned by trial and error.

• 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.

• 충청수학회지
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• 제30권3호
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• 충청수학회지
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• 제4권1호
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• pp.115-119
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• 1991

In this paper we obtain the asymptotic behavior of solutions of the perturbed system x' = (A(t) + B(t))x of x' = A(t)x by using the Floquet theorem.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.267-268
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• 2013

• 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.

• 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.