• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.287-296
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• 2003

We investigate global bifurcation in the motion of an harmonically excited circular plate with one-to-one internal resonance. A perturbation method developed by Kovacic and Wiggins is used. Silnikov type homoclinic orbit has been pursued but it has turned out not to exist.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.547-560
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• 1999

In this paper an asymptotic iteration method is adopted to analyze non-linear free vibration of reticulated circular plates composed of beam members placed in two orthogonal directions. For the resulting linear ordinary differential equations in the process of iteration, the power series with rapid convergence has been applied to obtain an analytical solution for non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating hardening of such structures have been presented for the (immovable or movable) simply-supported and clamped circular plates.

• Journal of Theoretical and Applied Mechanics
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• 제1권1호
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• pp.89-96
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• 1995

An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.140-144
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• 2004

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The Melnikov's method for heteroclinic orbits of the autonomous system was used to obtain the criteria for chaotic motion.

• 한국강구조학회 논문집
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• 제18권1호
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• pp.1-10
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• 2006

본 논문은 원형 판의 진동 해석에 미분변환법을 적용하였다. 계산된 수치적인 결과들은 이전의 연구결과들과 비교되었다. 그 결과를 기존의 연구 결과와 비교하여 미분변환법의 타당성을 검증하였고, 두께 형상과 경계조건 및 내경변화에 의한 고유진동수의 변화를 해석 및 고찰하였다. 유용성을 입증하였다.

• 소음진동
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• 제7권2호
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• pp.331-345
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• 1997

A theoretical formulation for the analysis of free vibration of clamped-free cylindrical shells with plates attached at arbitrary axial position(s) was completed and it was programed to get the numerical results which yield natural frequencies and mode shape of the combined system of the plate and the shells. The frequencies and mode shapes from theoretical calculation were compared with those of commercial finite element code, ANSYS. In order to validate the theory, modal test was also performed by impact test and FFT analysis. The results shows good agreement with those of ANSYS and test results in frequencies and mode shapes. The method developed herein is likely to be used for the analysis of the free vibration of the clamped-free circular cylindrical shells with any kinds of lids such as hollow circular plates, conical shells, spherical shells, or semi-spherical shells.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
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• pp.465-472
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• 1998

In this study, analytic solution and finite element formulation for the free vibration analysis of thin-walled circular arch, based on linearized virtual work and Vlasov's assumption, including restrained warping effect and second order terms of finite semitangential rotations, is presented. The total potential energy is derived by applying the Hellinger-Reissner principle. In this formulation, all displacement parameters of deformation are defined at the centroid axis. For the finite element formulation, the two node cubic Hermitian polynomials are utilized as shape functions. In special case, potential energy functional of thin-walled curved beam with monosymmetric cross section is derived. From this methodology, analytic solution for the free vibration of monosymmetric circular arch with simply supported is derived. In order to illustrate the accuracy of this study, various parameter studies for free vibration of circular arches are presented and compared with numerical solution analyzed by the FEM using straight beam element.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.609-616
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• 2001

The vibrational characteristics of nonuniform circular rods have been studied theoretically and experimentally in this paper. The differential equation of torsional motion expressed in terms of the angular displacement has been solved exactly and approximately for a stepped circular rod and for a conically-tapered rod. Solutions of the boundary-value problem have yielded the natural frequencies, mode shapes and forced responses of the rods. The theoretical solutions of forced response have been verified by comparing them with experimental ones.

• Steel and Composite Structures
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• 제33권2호
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• pp.163-180
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• 2019

A semi analytical method is employed to analyze free vibration characteristics of uniform and stepped functionally graded circular cylindrical shells under complex boundary conditions. The analytical model is established based on multi-segment partitioning strategy and first-order shear deformation theory. The displacement functions are handled by unified Jacobi polynomials and Fourier series. In order to obtain continuous conditions and satisfy complex boundary conditions, the penalty method about spring technique is adopted. The solutions about free vibration behavior of functionally graded circular cylindrical shells were obtained by approach of Rayleigh-Ritz. To confirm the dependability and validity of present approach, numerical verifications and convergence studies are conducted on functionally graded cylindrical shells under various influencing factors such as boundaries, spring parameters et al. The present method apparently has rapid convergence ability and excellent stability, and the results of the paper are closely agreed with those obtained by FEM and published literatures.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2010년도 춘계학술대회 논문집
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.