• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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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.

• Proceedings of the Korea Society for Simulation Conference
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• 1994.10a
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• pp.4-4
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• 1994

미분방정식은 많은 학문에서 현실 세계의 대상을 모형화하고 시뮬레이션하는 데에 매우 유용하게 사용되는 도구이다. 그 중에서도 현실 세계에서 적용되는 물리적 법칙에 근거해서 가상 세계를 만드는 컴퓨터 애니메이션이나 과학적 가시화등의 분양에서는 미분방정식으로 다루고자하는 대상을 모형화하고 시뮬레이션을 통해서 필요한 자료를 추출하는 과정이 필수적이다. 본 연구에서는 현실 세계에 근거한 가상세계를 만들기 위해서 요구되는 물리적 시뮬레이션을 수행하기 위한 방법을 연구하고, 그 소프트웨어를 개발한다. 현실세게를 모형화하는데에 많이 쓰이는 물리학적 방법은 역학에 근거한 미분방정식들이다. 그 중에서도 연립 상미분방정식의 형태로 많이 나타나는 Newton 방정식은 거시적인 물체들간의운동ㅇㄹ 표현하는데에 많이 사용도니다. 그리고 편미분방정식의 형태로 나타나는 Lagrange 방정식은 Hamilton의 원리를 운동방정식에 적용하여 얻은 것으로 Newton 방정식과 관계가 없는 광버무이한 물리적 현상을 표현하는데에 사용된다. 본 연구에서 개발하는 시물레이션 소프트웨어는 연립 상미분방정식으로 모형화되는 대상을 시뮬레이션할 수 있는 방법과 2c, 편미분방정식으로 모형화되는 대상을 시뮬레이션 할 수 있는 방법을 제공한다.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.730-735
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• 2013

This paper contains various vibration analysis of multi-stage shaft shape such as the bending, torsional and axial vibration. The shaft system is modeled as Timoshenko beam with the transverse shear and rotary inertia effect and the equation of motion is derived by Hamilton's principle with considering clamped-free boundary condition. Then, eigenvalue problem of discrete equation of motion for multi-stage shaft model is solved and got results of the natural frequency through the numerical analysis. Obtained numerical analysis results through Matlab program were compared with those of FEM analysis to verify the results. This study suggests that design of shaft system be consider torsional and axial vibration as well as bending vibration.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.387-392
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• 2004

The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton's principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, in which the Lyapunov function candidate is introduced from the total mechanical energy of the system. The performance of the proposed control law is compared with other two control algorithms available in the literature. Experimental results are given.

• Journal of Ocean Engineering and Technology
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• v.8 no.2
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• pp.151-156
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• 1994

The equations of motion of a submarine pipeline with the internal flowing fluid and subject to hydrodynamic loadings are derived by using Hamilton's principle. Coupling between the bending and the longitudinal extension due to axial load and thermal expansion are considered. Coupling between the twisting and extension are not considered. The equations of motion are well agreed with the results which are derived by the vector method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.2
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• pp.217-224
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• 2016

In this study, a transfer matrix method (TMM) for a twisted uniform beam considering the effect of rotary inertia is developed, and the differential equation and the displacements and forces are derived from Hamilton's principle. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. In addition, the results obtained from this method are independent for a number of subdivided elements, and this method can determine the exact solutions for the free vibration characteristics of a twisted uniform Rayleigh beam. To validate the accuracy of the proposed TMM, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of rotary inertia for a twisted beam.

• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.5-14
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• 1999

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Composites Research
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• v.29 no.6
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• pp.379-387
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• 2016

Structural model of laminated composite plate based on the first order shear deformation theory and subjected to a combination of piezoelectric, electromagnetic and thermal fields is established. Coupled equations of motion are derived via Hamilton's principle on the basis of electromagnetic and piezoelectric equations which are involved in constitutive equations. Proportional control and velocity feedback control logics are applied via boundary control moments and forces. Variations of dynamic chasracteristics of composite plate with collocated piezoelectric sensor and actuators, electromagnetic field and temperature gradient are investigated and it reveals that dynamic characteristics of structure can be effectively controlled by utilizing the piezoelectric effect and ply angles of fiber reinforced composites.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.372-377
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• 2001

A new non-linear 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 for 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 modeling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by $Pa{\ddot{i}}dousis$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.6
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• pp.2015-2025
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• 1991

A long and light-weight forearm of the vertical 2 DOF robot manipulator with a heavy payload driven by parallel drive mechanism is modelled as a Euler-Bernoulli beam with a tip mass subjected to a high speed rotation. Governing equation is obtained by Hamilton's principle and represented as state variable form using the perturbed variables which describe the perturbed errors at the manipulator's final configuration. Digitial optimal control and observer theory are used to suppress the forearm vibration and control the positions of the joint angles with measured/estimated state feedback. Computer simulations and experimental results are obtained and compared each other.