• 한국항해항만학회지
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• 제41권1호
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• pp.1-8
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• 2017

선체의 비선형적 동요현상은 선박의 감항성 확보와 관련하여 최근 활발하게 연구가 이루어지는 분야들 중 하나이다. 본 연구에서는 고차 스펙트럼 해석방법들 중 하나인 바이스펙트럼 해석방법과 바이코히어런스 해석방법을 적용하여 선체의 비선형적인 동요 현상을 해석하였다. 본 연구를 통해 기존에 알려진 추파상황에서의 비선형적 선체 종동요 현상과 더불어 추사파 및 우현 횡파 상황에서도 선체 종동요의 비선형 위상 동조 현상이 일어나는 것을 확인하였다. 또한, 바이코히어런스 방법을 통해 주파수간 비선형적 간섭현상을 수치화 하여 주파수 대역별로 위상 동조 현상을 비교할 수 있었다. 이를 통해 선체 종동요의 파워스펙트럼상의 피크 주파수 이외의 주파수 대역에서 비선형적 위상결합이 더 강하게 일어난다는 사실을 확인하였다. 이에 더하여, 바이코히어런스 해석방법은 정규화 방법에 크게 영향을 받지 않는 다는 사실 또한 확인하였다.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2006년도 Asia Navigation Conference
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• pp.134-143
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• 2006

Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. Den are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained form forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are compared with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.983-986
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• 2005

Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

• 한국컴퓨터산업학회논문지
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• 제8권3호
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• pp.181-186
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• 2007

폐쇄된 계 내부와 외부에서 작용되는 운동에는 선형 열린 운동과 닫힌 운동이 있고 비선형 열린 운동과 닫힌 운동이 있다. 선형 닫힌 운동이 마찰과 같은 외력을 받을시 갇힌 운동이 발생된다. 회전 닫힌 운동에도 마찰과 같은 외력을 받을시 회전 갇힌 운동이 있음을 해석 한다. 회전 닫힌 운동과 갇힌 운동을 액체 실험 장치를 통하여 정량적으로 고찰하고 회전 갇힌 운동이 있음을 분석하여 회전 열린 운동, 닫힌 운동 과 갇힌 운동에 대한 컴퓨터 씨뮬레이션 수식모델을 정한다. 그리고 간단한 운동 장치의 그래픽 구조를 고려 할 수 있도록 소개한다.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.597-605
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• 2015

In this study, linear vibrations of an axially moving beam under non-ideal support conditions have been investigated. The main difference of this study from the other studies; the non-ideal clamped support allow minimal rotations and non-ideal simple support carry moment in minimal orders. Axially moving Euler-Bernoulli beam has simple and clamped support conditions that are discussed as combination of ideal and non-ideal boundary with weighting factor (k). Equations of the motion and boundary conditions have been obtained using Hamilton's Principle. Method of Multiple Scales, a perturbation technique, has been employed for solving the linear equations of motion. Linear equations of motion are solved and effects of different parameters on natural frequencies are investigated.

• Steel and Composite Structures
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• 제24권2호
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• pp.141-149
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• 2017

In this study, vibration analysis of fluid conveying microbeams under non-ideal boundary conditions (BCs) is performed. The objective of the present paper is to describe the effects of non-ideal BCs on linear vibrations of fluid conveying microbeams. Non-ideal BCs are modeled as a linear combination of ideal clamped and ideal simply supported boundary conditions by using the weighting factor (k). Non-ideal clamped and non-ideal simply supported beams are both considered to show the effects of BCs. Equations of motion of the beam under the effect of moving fluid are obtained by using Hamilton principle. Method of multiple scales which is one of the perturbation techniques is applied to the governing linear equation of motion. Approximate solutions of the linear equation are obtained and the effects of system parameters and non-ideal BCs on natural frequencies are presented. Results indicate that, natural frequencies of fluid conveying microbeam changed significantly by varying the weighting factor k. This change is more remarkable for clamped microbeams rather than simply supported ones.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.289-294
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• 2001

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically. The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytic solutions of the system. The frequency-response curves show that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear phenomena.

• 한국소음진동공학회논문집
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• 제12권1호
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• pp.57-64
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• 2002

Three kinds of viscoelastic damper model, which has a non-linear spring as an element is studied analytically and numerically The behavior of the damper model shows non-linear hysteresis curves which is qualitatively similar to those of real viscoelastic materials. The motion is governed by a non-linear constitutive equation and an additional equation of motion. Harmonic balance method is applied to get analytical solutions of the system. The frequency-response curves sallow that multiple solutions co-exist and that the jump phenomena can occur. In addition, it is shown that separate solution branch exists and that it can merge with the primary response curve. Saddle-node bifurcation sets explain the occurrences of such non-linear Phenomena.

• 대한기계학회논문집A
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• 제26권3호
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• pp.514-520
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• 2002

A new non-linear modelling of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the generalized-$\alpha$ time integration method to the non-linear discretized equations. The validity of the new modelling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by Paidoussis.