• 한국해양공학회지
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• 제31권3호
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• pp.196-201
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• 2017

A cylindrical structure has a very long period of heave and pitch motion response in ocean waves. To obtain the dynamic stability of a cylindrical structure, it is necessary to obtain the suitable metacentric height (GM). However, in a structure with sufficient metacentric height, Mathieu instability can occur if the natural frequency of the heave motion is double the natural frequency of the roll and pitch motion. This study carried out numerical calculations and experiments for vertical-axis wind turbines with cylindrical floaters, which had three different centers of gravity. In the regular wave experiment, the divergence of the structure motion without yaw was observed when the natural frequency of the heave motion was double the natural frequency of the roll and pitch motion. In the irregular wave experiment, the motion spectra of the structures with the different centers of gravity were compared, and one was very high when the natural frequency of the heave motion was double the natural frequency of the roll and pitch motion.

• 대한조선학회논문집
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• 제28권1호
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• pp.69-82
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• 1991

축방향의 주기적인 하중으로 가진되는 긴 수직보의 동적안정성에 관하여 연구하였다. 해석방법으로서 Galerkin방법을 이용하여 무한원 연립 Mathieu형 미분 방정식을 얻었으며, 안정성영역을 나타내는 도표를 얻기 위하여, 섭동법과 수치적인 방법을 사용하였다. 또한 이두가지 방법으로 구한 결과를 서로 비교 검토하였다. 여러가지 경계조건에 대한 안정영역을 구했으며, 김쇠의 영향, 평균인장력 및 다중 주파수 파라메터 기진의 영향에 관해서 집중적으로 연구하였다.

• Advances in aircraft and spacecraft science
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• 제6권4호
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• pp.297-314
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• 2019

Dynamic stability of a porous metal foam nano-dimension plate on elastic substrate exposed to bi-axial time-dependent forces has been studied via a novel 3-variable plate theory. Various pore contents based on uniform and non-uniform models have been introduced. The presented plate model contains smaller number of field variables with shear deformation verification. Hamilton's principle will be utilized to deduce the governing equations. Next, the equations have been defined in the context of Mathieu-Hill equation. Correctness of presented methodology has been verified by comparison of derived results with previous data. Impacts of static and dynamical force coefficients, non-local coefficient, foundation coefficients, pore distributions and boundary edges on stability regions of metal foam nanoscale plates will be studied.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 춘계학술대회논문집
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• pp.695-700
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• 2000

The dynamic stability of spinning beam with free boundary conditions for both edges subjected to a tip follower force $P_0+P_1cos{\Omega}t$ is analyzed. It is studied that the beam has a concentrated mass. and then the effects of the axial locations of the mass are studied. The beam is modelled with the Timoshenko type shear deformations. The Hamilton's principle is used to derive the equations of motion, and the critical spinning speed of a beam subjected to a follower force with various non-dimensional parameters is investigated. The finite elements are used with $C^0$ continuity to analyze the spinning beam model, and the method of multiple scales is tried to investigate the dynamic instability regions. The governing equations of motion involve periodic coefficients, which are not in the form of standard Mathieu-Hill equations. The result shows that the concentrated mass increases the dynamic stability of the spinning free-free beam subjected to a thrust.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.181-189
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).

• Structural Monitoring and Maintenance
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• 제7권1호
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• pp.27-42
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• 2020

Dynamic stability of graded nonlocal nano-dimension plates on elastic substrate due to in-plane periodic loads has been researched via a novel 3- unknown plate theory based on exact position of neutral surface. Proposed theory confirms the shear deformation effects and contains lower field components in comparison to first order and refined 4- unknown plate theories. A modified power-law function has been utilized in order to express the porosity-dependent material coefficients. The equations of nanoplate have been represented in the context of Mathieu-Hill equations and Chebyshev-Ritz-Bolotin's approach has been performed to derive the stability boundaries. Detailed impacts of static/dynamic loading parameters, nonlocal constant, foundation parameters, material index and porosities on instability boundaries of graded nanoscale plates are researched.

• International Journal of Naval Architecture and Ocean Engineering
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• 제8권1호
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• pp.13-21
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• 2016

Parametric pitch instability of a Deep Draft Semi-submersible platform (DDS) is investigated in irregular waves. Parametric pitch is a form of parametric instability, which occurs when parameters of a system vary with time and the variation satisfies a certain condition. In previous studies, analyzing of parametric instability is mainly limited to regular waves, whereas the realistic sea conditions are irregular waves. Besides, parametric instability also occurs in irregular waves in some experiments. This study predicts parametric pitch of a Deep Draft Semi-submersible platform in irregular waves. Heave motion of DDS is simulated by wave spectrum and response amplitude operator (RAO). Then Hill equation for DDS pitch motion in irregular waves is derived based on linear-wave theory. By using Bubnov-Galerkin approach to solve Hill equation, the corresponding stability chart is obtained. The differences between regular-waves stability chart and irregular-waves stability chart are compared. Then the sensitivity of wave parameters on DDS parametric pitch in irregular waves is discussed. Based on the discussion, some suggestions for the DDS design are proposed to avoid parametric pitch by choosing appropriate parameters. The results indicate that it's important and necessary to predict DDS parametric pitch in irregular waves during design process.

• 대한기계학회논문집A
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• 제26권12호
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• 대한기계학회논문집B
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• 제38권10호
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• pp.845-851
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• 2014

유전영동(DEP)이란 비균질의 전기장과 그에 따라 입자 내부에 형성되는 극성힘에 의해 용매에 분산되어 있는 입자에 야기되는 운동을 의미하며, 세포, 바이러스, 나노입자 등의 트래핑, 입자분류, 셀분리 등과 같은 다양한 생물학적 응용에 이용되어 왔다. 지금까지 유전영동트랩에 대한 해석은 주기평균 ponderomotive force 에 기반한 정특성 해석이 주를 이루고 있으며, 동특성에 대해서는 많은 연구가 이루어져 있지 않다. 이는 지금까지 유전영동트랩이 적용된 입자들의 크기가 상대적으로 매우 크기 때문으로, 분석입자의 크기가 매우 작은 나노단위 분석에서는 적절하지 않다. 본 연구에서는, 다양한 시스템 파라미터들에 대한 트래핑의 동역학적 반응 및 그들의 트래핑 안정성에 대한 영향을 심도깊게 관찰하고자 한다. 특히, 입자의 전도율에 따른 입자의 동특성의 변화 또한 관찰하고자 한다.

• International Journal of Aeronautical and Space Sciences
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• 제14권1호
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• pp.19-29
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• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.