• Title, Summary, Keyword: Equation of Motion

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Self-similarity in the equation of motion of a ship

  • Lee, Gyeong Joong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.6 no.2
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    • pp.333-346
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    • 2014
  • If we want to analyze the motion of a body in fluid, we should use rigid-body dynamics and fluid dynamics together. Even if the rigid-body and fluid dynamics are each self-consistent, there arises the problem of self-similar structure in the equation of motion when the two dynamics are coupled with each other. When the added mass is greater than the mass of a body, the calculated motion is divergent because of its self-similar structure. This study showed that the above problem is an inherent problem. This problem of self-similar structure may arise in the equation of motion in which the fluid dynamic forces are treated as external forces on the right hand side of the equation. A reconfiguration technique for the equation of motion using pseudo-added-mass was proposed to resolve the self-similar structure problem; specifically for the case when the fluid force is expressed by integration of the fluid pressure.

Random Analysis of Rolling Equation of Motion of Ships Based on Moment Equation Method (모멘트 방정식 방법에 의한 횡요 운동 방정식의 램덤 해석)

  • 배준홍;권순홍;하동대
    • Journal of Ocean Engineering and Technology
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    • v.6 no.2
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    • pp.41-45
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    • 1992
  • In this paper an application technique of moment equation method to solution of nonlinear rolling equation of motion of ships is investigated. The exciting moment in the equation of rolling motion of ships is described as non-white noise. This non-white exciting moment is generated through use of a shaping filter. These coupled equations are used to generate moment equations. The nonstationary responses of the nonlinear system are obtained. The results are compared with those of a linear system.

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SINGULAR PERIODIC SOLUTIONS OF A CLASS OF ELASTODYNAMICS EQUATIONS

  • Yuan, Xuegang;Zhang, Yabo
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.501-515
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    • 2009
  • A second order nonlinear ordinary differential equation is obtained by solving the initial-boundary value problem of a class of elas-todynamics equations, which models the radially symmetric motion of a incompressible hyper-elastic solid sphere under a suddenly applied surface tensile load. Some new conclusions are presented. All existence conditions of nonzero solutions of the ordinary differential equation, which describes cavity formation and motion in the interior of the sphere, are presented. It is proved that the differential equation has singular periodic solutions only when the surface tensile load exceeds a critical value, in this case, a cavity would form in the interior of the sphere and the motion of the cavity with time would present a class of singular periodic oscillations, otherwise, the sphere remains a solid one. To better understand the results obtained in this paper, the modified Varga material is considered simultaneously as an example, and numerical simulations are given.

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Swing Motion Analysis of the Container Crane Headblock (콘테이너 크레인의 헤드블록 횡동요 해석)

  • 조대승
    • Journal of KSNVE
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    • v.7 no.5
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    • pp.765-772
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    • 1997
  • This paper presents the swing motion analysis of the container crane headblock with the passive control device using hydraulic motors and anti-swing ropes. The device hauls at the headblock to opposite direction of its swing motion using the tension difference between anti-swing ropes connected to the headblock. To consider this control mechanism, the headblock is modelled as the rigid bar suspended by two hoist ropes at the overhead trolley and its non-linear equation of motion is derived using Lagrange's equation. Some numerical experiments using the equation are carried out to investigate the swing motion characteristics of the headblock under the variation of geometric relation among the cargo handling components and to evaluate the performance of the anti-swing device.

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Identification of Linear Structural Systems (선형 구조계의 동특성 추정법)

  • 윤정방
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.46-50
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    • 1989
  • Methods for the estimation of the coefficient matrices in the equation of motion for a linear multi-degree-of-freedom structure arc studied. For this purpose, the equation of motion is transformed into an auto-regressive and moving average with auxiliary input (ARMAX) model. The ARMAX parameters are evaluated using several methods of parameter estimation; such as toe least squares, the instrumental variable, the maximum likelihood and the limited Information maximum likelihood methods. Then the parameters of the equation of motion are recovered therefrom. Numerical example is given for a 3-story building model subjected to an earthquake exitation.

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Chaotic Vibration of a Curved Oipe Conveying Oscillatory Flow (조화진동유동을 포함한 곡선파이프계의 혼돈운동 연구)

  • 박철희;홍성철;김태정
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.288-294
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    • 1996
  • In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

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Historical Background for Derivation of the Differential Equation mẍ+kx = f(t) (미분방정식 mẍ + kx = f(t)의 역사적 유도배경)

  • Park, Bo-Yong
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.4
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    • pp.315-324
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    • 2011
  • This paper presents a historical study on the derivation of the differential equation of motion for the single-degree-of-freedom m-k system with the harmonic excitation. It was Euler for the first time in the history of vibration theory who tackled the equation of motion for that system analytically, then gave the solution of the free vibration and described the resonance phenomena of the forced vibration in his famous paper E126 of 1739. As a result of the chronological progress in mechanics like pendulum condition from Galileo to Euler, the author asserts two conjectures that Euler could apply to obtain the equation of motion at that time.

A Prediction of the Equation of Resistance to Motion for Korean High-speed Train (한국형 고속열차의 주행저항식 예측)

  • Kwon, Hyeok-Bin;Kim, Seog-Won;Kim, Young-Guk;Park, Chool-Soo
    • Proceedings of the KSR Conference
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    • pp.119-125
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    • 2007
  • The equation of Resistance to motion of the Korean high-speed train has been calculated and evaluated using train speed measurements gathered from coasting tests in the speed range from 30km/h to 300km/h and wind tunnel test of 1/25th scale model. The factors of resistance to motion have been decomposed into various coefficients which compose the coefficients of Davis equation referring the general resistance to motion equation of KTX train. The coefficients of Korean high-speed train has been calculated using the measurements of coasting tests and the results of wind tunnel test has been implemented to consider the minor shape modification after the coasting tests.

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Chaotic Vibration of a Straight Pipe Conveying Oscillatory Flow (조화진동유동을 포함한 직선파이프계의 혼돈운동 연구)

  • Pak, Chul-Hui;Hong, Sung-Chul;Jung, Wook
    • Journal of KSNVE
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    • v.6 no.2
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    • pp.233-244
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    • 1996
  • In this paper chaotic mothions of a straight pipe conveying oscillatory flow and being subjected to external forces such as earthquake are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. In this equation, the nonlinear curvature of the pipe and the thermal expansion effects are contained. The nonlinear ordinary differential equation transformed from that partial differential equation is a type of Hill's equations, which have the parametric and external exciation term. This original system is transfered to the averaged system by the averaging theory. Bifurcation curves of chaotic motion of the piping system are obtained in the general case of the frequency ratio, n by applying Melnikov's method. Numerical simulations are performed to demonstrate theorectical results and show strange attactors of the chaotic motion.

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