• 한국해양공학회지
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• 제10권3호
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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.

• Advances in concrete construction
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• 제15권2호
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• pp.137-147
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• 2023

Dynamic analysis of a shear deformable shell is investigated with accounting thickness stretching using Hamilton's principle. Through this method, the total transverse is composed into bending, shearing and stretching portions, in which the third part is responsible for deformation along the transverse direction. After computation of the strain, kinetic and external energies, the governing motion equations are derived using Hamilton's principle. A comparative study is presented before presentation of full numerical results for confirmation of the formulation and methodology. The results are presented with and without thickness stretching to show importance of the proposed theory in comparison with previous theories without thickness stretching.

• 한국공간구조학회논문집
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• 제14권1호
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• pp.101-108
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• 2014

In order to overcome the key shortcoming of Hamilton's principle, recently, the extended framework of Hamilton's principle was developed. To investigate its potential in further applications especially for material non-linearity problems, the focus is initially on a classical single-degree-of-freedom elasto-viscoplastic model. More specifically, the extended framework is applied to the single-degree-of-freedom elasto-viscoplastic model, and a corresponding weak form is numerically implemented through a temporal finite element approach. The method provides a non-iterative algorithm along with unconditional stability with respect to the time step, while yielding whole information to investigate the further dynamics of the considered system.

• 한국전산구조공학회논문집
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• 제29권5호
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• pp.421-428
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• 2016

논문은 동역학의 새로운 변분이론인 확장 해밀턴 이론을 열 탄성과 공극 탄성에 적용하여 더욱 일반화하는 것에 그 주요 목적이 있다. 이를 위해 열 탄성학에 대한 이론 적용이 우선적으로 검토되었고, 열 탄성-공극 탄성의 유사성을 바탕으로 공극 탄성에까지 그 이론이 확장되었으며, 각 경우에 대한 푸리에 변환을 통해 그 적정성을 확인하였다.

• Journal of Theoretical and Applied Mechanics
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• 제1권1호
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• pp.1-27
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• 1995

In this paper a finite element method for free-surface problems is described. the method is based on two different forms of Hamilton's principle. To test the present computational method two specific wave problems are investigated; the dispersion relations and the nonlinear effect for the well-known solitary waves are treated. The convergence test shows that the present scheme is more efficient than other existing methods, e.g. perturbation scheme.

• 한국전산구조공학회논문집
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• 제27권1호
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• pp.37-43
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• 2014

동역학의 새로운 변분이론인 확장 해밀턴 이론은 수학물리학을 비롯한 공학에 있어 초기치-경계치 문제해석에 광범위하게 적용될수 있는 기반을 제공하는 것으로 본 논문에서는 이 이론을 기반으로 선형탄성 단자유도계에 적용한 새로운 수치해석법을 제안하였다. 곧, 변분이론의 특성을 감안해, 전체 time-step에 대한 수치해를 한번에 산정하는 해석법을 제안하였고, 주요 예제를 통해 이 해석법의 특성을 살펴보았다. 에너지 보존 시스템의 경우(비감쇠 시스템에 외력이 작용치 않는 경우), time-step에 관계없이 에너지와 모멘텀이 보존되는 symplecticity property를 가지고 있음을 확인할 수 있었고, 감쇠 시스템인 경우, time-step이 점점 작아질수록 정확한 해에 빠르게 수렴하는 것을 확인하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집B
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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.

• 한국정밀공학회지
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• 제12권2호
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• pp.14-22
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• 1995

We treat the vibrations of circular beam and make use of the method employed by J.T.Tielking, which is based on the principle of Hamilton. The Hamilton's principle requires the determinations of the potential and the kinetic energy of the model as well as done by internal pressure forces. Thje potential energy is composed of a part due to elastic deformations of the beam and a part due to radial and tangential displacements of the tread band with respect to the wheel rim. The equations of motion for such a model are derived by reference to conventional energy method. The accuracy of the expressions is demonstrated by comparison of calculated and experimental natural frequencies for circular beam. The circular beam experiences a harmonic, radial excitat- ion acting at a fixed point on the beam. Modal parameters varying the inflation pressure and load are determined experimentally by using the transfer function method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.619-624
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• 2007

Spectral element method (SEM) is introduced for the fully coupled structural dynamic problems, In this paper, the beam with passive constrained layered damping (PCLD) treatments is considered as a representative problems. The beam consists of a viscoelastic layer that is sandwiched between the base beam structure and an elastic layer, The fully coupled equations of motion for a PCLD beam are derived, The equations of motion are derived first by using Hamilton's principle, From this equations of motion, the spectral element is formulated for the vibration analysis by use of the SEM, As an illustrative example, a cantilevered beam is considered. It is shown that, as the thickness of VEM layer vanishes, the results become a simple layer beam's that.

• Structural Engineering and Mechanics
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• 제71권5호
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• pp.459-467
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• 2019

In this paper, hyperbolic shear deformation theory is used for free vibration analysis of piezoelectric rectangular plate made of porous core. Various types of porosity distributions for the porous material is used. To obtain governing equations of motion, Hamilton's principle is used. The Navier's method is used to obtain numerical results of the problem in terms of significant parameters. One can conclude that free vibration responses are changed significantly with change of important parameters such as various porosities and dimensionless geometric parameters such as thickness to side length ratio and ratio of side lengths.