• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.96-104
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• 1996

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1587-1600
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• 1991

본 연구에서는 로봇조작기를 강체부와 유연한 외팔보로 이루어진 모델로 설정 한 후 확장된 Hamilton의 원리를 적용하여 제어계의 운동방정식을 유도하였다. 계를 유한개의 제어 모드와 잔류 모드로 구분하고, 제어 모드에 대해 최적제어를 수행하기 위해 관측기를 설계하였으며, 진동에 관련된 측정 불가능한 상태변수를 추정하였다. 분석과 검토는 서보모터가 모든 제어를 담당하는 방식과 서보모터의 제어 방식에 작동 기를 추가시켜 병행 제어하는 다입출력 방식으로 구별하여 수행하였다.

• Proceedings of the KAIS Fall Conference
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• 2009.05a
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• pp.528-531
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• 2009

본 연구에서는 두 스프링으로 지지된 강체가 회전하는 Timoshenko 축을 따라 이동할 때, 그 계의 동적응답 특성을 해석하였다. 운동방정식은 Hamilton의 원리에 따라 유도되었다. 유도된 운동방정식을 이용하여 주요 설계 파라미터 변화에 따른 응답특성을 해석하였다. 해석시 설계파라미터를 무차원 변수화 하여 속도비, 질량비, 회전수비 등 그 변화에 따른 응답특성을 비교 분석하였다.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.658-663
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• 2001

The dynamic response of an axially deploying beam is studied when the beam has geometric non-linearity and translating acceleration. Based upon the von Karman strain theory, the governing equations and the boundary conditions of a deploying beam are derived by using extended Hamilton's principle considering the longitudinal and transverse deflections. The equations of motion are discretized by using the Galerkin approximate method. From the discretized equations, the dynamic responses are computed by the Newmark time integration method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.478-487
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• 1991

In this study, dynamic stability of discontinuous free Timoshenko beam, barring a concentrated mass, under constant follower force is considered. Governing differential equations are derived based on the extended Hamilton's principle and finite element method is applied for numerical analysis. Conclusions of the study are as follows : (1) Without force direction control, (i) the critical follower force at instability is increased with concentrated mass regardless of discontinuity. (ii) the minimum critical follower force is located in the vicinity of discontinuity position .xi.$_{d}$=0.75. (iii) at mass location .mu. .leq.0.5 the force at instability is decreased as magnitude of concentrated mass is increased but, at .mu. .geq. 0.5 the force is increased as the mass is increased. (2) With force direction control, (i) shear deformation parameter S contributes insignificantly to the force at instability when S>10$^{[-993]}$ (ii) maximum critical follower force can be obtained for the discontinuity location .xi.$_{d}$=0.25. (iii) the critical follower force is increased as magnitude of concentrated mass .alpha. is increased at mass location .mu. .geq.0.4, but is increased, .mu ..leq.0.4.4.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.3
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• pp.19-30
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• 1990

This note describes an application of Hamiton's principle to nonlinear free-surface flow problems. Two functionals are constructed based on classical Hamilton's principle with a modification due to the presence of a free surface. As an effort towards the development of an efficient numerical scheme for our problem, we present the following three test results: i) The bounding principles of the eigenvalues for the linear dispersion relation. ii) By assuming steady solitary waves, an approximate relation between the amplitudes and the speeds of solitary waves are derived from the two functionals constructed. Their numerical results are compared with those of Longuet-Higgins & Fenton(1974). iii) The shapes and charicteristics of solitary waves are computed from two sets of functionals by varying the number of total finite elements in the fluid domain.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.923-934
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• 1987

A flexible one-link robotic manipulator is modelled as a rotating cantilever beam with a hub and tip mass. An active control law is developed with consideration of the distributed flexibility of the arm. Equation of motion is derived by Hamilton's principle and, for modal control, represented as state variable form using Galerkin's mode summation method. Feedback coefficients are chosen to minimize the linear quadratic performance index(PI). To reconstruct the complete state vector from the measurements, an observer is proposed. In order to suppress vibration of the manipulator arm to desirable extent and to obtain accuracy of the positioning, weighting factor of input in PI is adjusted. Spillover effect due to the controller which controls several important modes is examined. Experiment is also performed to validate the theoretical analysis.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.2
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• pp.435-442
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• 2010

The analysis of rigid body traveling along the rotating Timoshenko shaft has been a topic of interest. The problem arose from the observations that as a structure is subjected to moving loads, dynamic deflection as well as stresses can be significantly higher than those for static loads. The establishment of analytical method for the development and maintenance of performance is required in the fields of the machining operations and the position control using ball screw. The equations of motion for the rotating shaft subjected to the two moving forces are derived by using Hamilton's principle. Influence of system parameters such as the speed ratio, the mass ratio and the Rayleigh coefficient is discussed on the response of the moving system.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.6 s.46
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• pp.1-12
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• 2005

For a shear-deformable beam-column element subjected io non-conservative forces, equations of motion and a finite element formulation are presented applying extended Hamilton's principle. The influence of non-conservative force's direction parameter, internal and external damping forces, and shear deformation and rotary inertia effects on divergence and flutter loads of Beck's columns are intensively investigated based on element stiffness, damping and mass matrixes derived for the non-conservative system.