• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.529-534
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• 2000

A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modelling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, are derived two weak forms: one is for the chordwise motion and the other is for the flapwise motion. The weak forms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviours of the natural frequencies are investigated for the variation of the rotating speed.

• 대한기계학회논문집A
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• 제26권1호
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• pp.61-66
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• 2002

The nonlinear differential equations of motion of a fluid conveying curved pipe are derived by use of Hamiltonian approach. The extensible dynamics of curled pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the dynamic characteristics are discussed. Generally, it can be shown that the natural frequencies in curved pipes are changed with flow velocity. Linearized natural frequencies of nonlinear equations are slightly different from those of linear equations.

• 대한전자공학회논문지
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• 제16권5호
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• pp.18-26
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• 1979

본 논문에서는 algebraic matrix Lyapunov equations과 a1gebraic matrix Riccati equations에 관하여 잘 알려져 있는 중요한 결과를 확장한다. 본 연구는 Matrix 미분 방정식에서 양단 경계조건이 존재하는 문제를 다루며 여기에서 얻어지는 결과는 기존하고 있는 결과를 포함하게 된다. 특히 선형 시스템이 periodic feedback gain control로 안정화되는 필요충분조건을 구하며, two-point boundary Riccati equations의 해를 쉽게 구하는 반복 계산방법을 제시한다. 또한 interalwise reeceding horizon을 이용한 새로운 periodic feedback gain control이 시스템을 안전화시켜줌을 보여준다.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.869-881
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• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• 대한수학회논문집
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• 제18권3호
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• pp.559-568
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• 2003

We introduce the notion of two-scale convergence for partial differential equations with random coefficients that gives a very efficient way of finding homogenized differential equations with random coefficients. For an application, we find the homogenized matrices for linear second order elliptic equations with random coefficients. We suggest a natural way of finding the two-scale limit of second order equations by considering the flux term.

• 자원환경지질
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• 제52권4호
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• pp.291-297
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• 2019

단열을 통한 유체의 유동은 선형유동이 우세하다는 가정아래 Navier-Stokes 방정식에서 유도된 Stokes 방정식, Reynolds 식(또는 local cubic law), cubic law 와 같은 방정식을 이용하여 해석되고 있다. 하지만 이러한 방정식은 선형 흐름에 국한되며, 비선형 유동영역에 적용하게 되면 오류가 발생한다. 본 연구에서는 레이저 계측기를 이용하여 정밀하게 측정한 3차원 단열 자료와 Navier-Stokes 방정식과 Stokes 방정식을 지배방정식으로 한 수치모델링을 수행함으로써 비선형 유동이 일어나는 현상과 임계 레이놀즈수를 제시하였다. 레이놀즈수가 10이상이 되면 유속의 제곱에 비례하는 관성력이 점성력을 충분히 압도할 정도로 커지면서 지하수 유동이 선형영역에서 비선형 유동영역으로 전환되는 것으로 분석되었다. 이는 평균 간극과 거친 정도가 다른 두 단열에서 모두 동일하게 나타났다. 비선형 유동의 발생기작은 소용돌이 구조의 발생과 성장에 의한 것으로 알려져 있지만, 본 연구결과 단순히 소용돌이 구조가 비선형 유동을 일으키는 아니라 유속이 증가하면서 관성력의 영향이 훨씬 큰 영향을 끼치게 되어 비선형 유동이 발생하는 것으로 나타났다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.162-165
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• 1995

For an accurate on-line measurement of the ship's attitude the paper develops an intelligent sensing system which uses one servo-type accelerometer and two servo-type inclinometers appropriately located on the ship. By considering the dynamics of the servo-controlled rigid pendulums of the inclinometers, linear equations for the rolling and pitching of the ship are derived separately from each other. Moreover, one accelerometer is used for extracting the heaving signal. Through the introduction of linear dynamic models and the linear observation equations for the heaving, rolling and pitching, the on-line measurement of the three signals can be reduced to the state estimation of the linear dynamic systems. A bank of Kalman filters is adaptively used to achieve the on-line accurate state estimation and to overcome changes in parameters in the linear dynamic models.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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• pp.319-324
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• 2001

Free non-linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in-plane and out-of-plane motions. The geometric non-linearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton's principle, the coupled non-linear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from three non-linear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the non- linear behavior more precisely.

• Structural Engineering and Mechanics
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• 제34권4호
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• 전력전자학회논문지
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• 제4권6호
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• pp.554-560
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• 1999

리니어 스텝핑 모터(Linear Stepping Motor : 이하 LSM이라 칭함)는 운동 변환기구 없이 입력신호에 따라 선형적인 변위를 발생시키는 다이렉트 드라이브(Direct Drive)방식의 전동기이다. 따라서 LSM은 자동반송장치, 의료기기, OA,FA 응용 등에 다양하게 사용되고 있다. 그러나 LSM은 구동시 구조적으로 큰 진동이 발생됨으로서 추력이 급격히 떨어질 때가 있으며, 최악의 경우에는 역전이나 탈조현상이 발생하고, 또한 소음의 원인이 되기 때문에 응용에 있어서 많은 제약을 받고 있는 실정이다. 여기에 대응하기 위해, 본 논문에서는 권선 인덕턴스에 저장된 에너지와 LSM의 유도전압을 이용한 새로운 1상 여자방식에 의한 진동억제 방법을 보여주며, 또한 LSM의 구조를 기초로 자기등가회로를 구성하였으며, 또한 자기등가회로에 대한 방정식을 이용하여 LSM의 전기적인 등기회로를 유도하였다. 그리고, LSM의 새로운 1상 여자방식에 의한 진동특성을 전압방정식과 추력방정식 및 운동방정식을 사용하여 ACSL에 의하여 시뮬레이션 하였으며, 레이저 실측 시스템에 의한 실측결과와 비교·검토하였다.