• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.1
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• pp.61-66
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• 2002

The nonlinear differential equations of motion of a fluid conveying curved pipe are derived by use of Hamiltonian approach. The extensible dynamics of curled pipe is based on the Euler-Bernoulli beam theory. Some significant differences between linear and nonlinear equations and the dynamic characteristics are discussed. Generally, it can be shown that the natural frequencies in curved pipes are changed with flow velocity. Linearized natural frequencies of nonlinear equations are slightly different from those of linear equations.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.3
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• pp.221-227
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• 2002

The longitudinal and lateral in-plane vibrations of an axially moving membrane are investigated when the membrane has translating acceleration. By extended Hamilton's principle, the governing equations are derived. The equations of motion for the in-plane vibrations are linear and coupled. These equations are discretized by using the Galerkin approximation method after they are transformed into the variational equations, j.e., the weak forms so that the admissible functions can be used for the bases of the in-plane deflections. With the discretized equations for the in-plane vibrations, the natural frequencies and the time histories of the deflections are obtained.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• Journal of the Korean Society of Hazard Mitigation
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• v.8 no.3
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• pp.129-136
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• 2008

All measures to cope with flooding rely on flood predictions to some extent. To investigate these predictions such as maximum water level or inundation area, a numerical model has been developed. The governing equations of the model are the two-dimensional Saint-Venant equations. The governing equations are discretized explicitly by using the leap-frog scheme and upwind scheme based on quadtree grids. The predicted numerical results have been verified by comparing to those of a Thacker problem. As a result of verifications, the present model is not only nearly four times as efficient as uniform grids but also in close agreement with the previous models. Next, the developed model is applied to several flood events in the Uiryeong basin. A general tendency is found that as a frequency is increasing, overall water levels including peak water level are increasing. At only a 500 year frequency, maximum water level is higher than 18.5 m. Therefore, it can be predictable that inundation will be generated in a 500 year frequency.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.22 no.1
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• pp.107-111
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• 2013

The gyroscopes have been used as a suitable inertial instrument for the navigation guidance and attitude controls. The accuracy as very sensitive sensor is limited by the lock-in region (dead band) due to the frequency coupling between two counter-propagating waves at low rotation rates. This frequency coupling gives no phase difference, and an angular increment is not detected. This problem can be overcome by mechanically dithering the gyroscope. This paper presents the design method of mechanical dither by the theoretical considerations and the verification of the theoretical equations through FEM applications. As a result, comparing to the past result, the maximum prediction error of resonant frequency was within 3 percent and peak dither rate was within 5 percent. It was found that the theoretical equations can be feasible for the mechanical performance of dither.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.6
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• pp.1949-1954
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• 2010

The gyroscopes have been used as a suitable inertial instrument for the navigation guidance and attitude controls. The accuracy as very sensitive sensor is limited by the lock-in region(dead band) due to the frequency coupling between two counter-propagating waves at low rotation rates. This frequency coupling gives no phase difference, and an angular increment is not detected. This problem can be overcome by mechanically dithering the gyroscope. This paper presents the design method of mechanical dither by the theoretical considerations and the verification of the theoretical equations through FEM(Finite Element Method) applications. As a result, the maximum prediction error of resonant frequency and peak dither rate was under 5 percent. The theoretical equations for the mechanical performances of dither can be said to be feasible.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.367-377
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• 2002

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations we assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Two arch shapes with hinged-hinged and clamped-clamped end constraints we considered in analysis. The frequency equations (lowest symmetrical and antisymmetrical frequency equations) we obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated. The effect of initial arch shapes on frequencies is also studied.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.9
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• pp.935-942
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• 2009

In this paper, the purpose is to investigate the natural frequency of a cracked Timoshenko cantilever beams by FEM(finite element method) and experiment. In addition, a method for detection of crack in a cantilever beams is presented based on natural frequency measurements. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The detection method of a crack location in a beam based on the frequency measurements is extended here to Timoshenko beams, taking the effects of both the shear deformation and the rotational inertia into account. The differences between the actual and predicted crack positions and sizes are less than 6 % and 23 % respectively.