• Journal of Navigation and Port Research
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• v.41 no.1
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• pp.1-8
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• 2017

The estimation of non-linear ship motion is one of the most important issues in recent studies of ship stability. In this paper, bispectral analysis and bicoherence analysis were introduced in order to analyze the non-linear ship motion. In addition to the previously observed non-linear pitching motion in following seas, this study observed the non-linear phase coupling of pitching motion in following & quartering seas, and starboard beam seas. By comparing phase coupling between each frequency quantitatively via the bicoherence analysis, it was confirmed that non-linear phase coupling was much stronger in frequency regions other than the peak frequencies of a power spectrum. Furthermore, it was found out that the results of bicoherence calculation were analagous to each other, although the different normalization methods were applied.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2006.10a
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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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.

• Journal of the Korea Computer Industry Society
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• v.8 no.3
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• pp.181-186
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• 2007

The movement in the closed system's internal and external, consists of linear open motion and linear closed motion, as well as non-linear motion and non-linear closed motion. When the linear closed motion receives external forces such as friction, closed motion is activated. It explains that even closed rotating systems that are subjected to external forces such as friction becomes a confined rotating system. Through fluid experiments the closed rotating system and confined system's quantitative data was observed and closed rotating system was confirmed to formulate the computer simulation function model concerning closed motion and confined motion. A basic graphic configuration of the motion device is also introduced.

• Structural Engineering and Mechanics
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• v.54 no.3
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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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• v.24 no.2
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.3
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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.