• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.3 s.120
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• pp.220-225
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• 2007

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

• Journal of Korean Society of Steel Construction
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• v.12 no.2 s.45
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• pp.221-230
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• 2000

Checking the stability of anisotropic plates with free edges, it is impossible that buckling loads and modes are found via existing classical methods about various loads and boundary conditions. For solving this problems. finite difference method(FDM) is used to analyze the buckling behaviors for arbitrary boundary conditions. Using FDM, it is difficult to treat the fictitious points on free edges. So, this paper analyzes buckling behaviors of analytic models with one edge free and the other edges clamped and with opposite two edges free and other two edges clamped. The various buckling loads and mode characteristics through numerical results are given for buckling behaviors of anisotropic plates on free edges.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1900-1907
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• 1992

This paper presents the vibration mode, natural frequencies and amplitudes of the circular plate due to the changes of the boundary conditions by varying free arc angles. The vibration mode, amplitudes and natural frequencies of the circular plate are obtained by time-average holographic interferometry and laser doppler vibrometer. The vibration modes of the circular plate with the mixed boundary conditions are found from the 1st mode to the 4th mode. The curve shapes of the natural frequency ratios obtained from this study are in a good agreement with other results obtained by numerical analysis. The displacement curves obtained from time average holographic interferometry and laser doppler vibrometer agree well in case of large amplitude, but show a little difference in case of small amplitude.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.740-745
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• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method is based on the collocation method, no integration procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is required. A special coordinate transformation has been devised to consider the complicated free boundary conditions at boundary nodes. By the use of the special coordinate transformation, the radius of curvature involved in the free boundary conditions can be successfully dealt with. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by exact method and other analytical methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.821-827
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• 2003

The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method requires no interpolation functions. no integration Procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is involved, compared with FEM and BEM. In order to explain tile reason why spurious eigenvalues are generated when the NDIF method is applied to free plates, the NDIF method has been considered for free vibration analysis of both a fixed string and a free beam. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by an exact method or a numerical method (ANSYS).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.35 no.2
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• pp.41-48
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• 2023

In this study, simplified linear numerical method that can simulate wave generation and transformation by a moving bottom is introduced. Numerical analysis is conducted in wave number domain after continuity equation, linear dynamic and kinematic free surface boundary conditions and linear kinematic bottom boundary condition are Fourier transformed, and the results are expressed in space domain by an inverse Fourier transform. In the wavenumber domain, the dynamic free water surface boundary condition and the kinematic free water surface boundary condition are numerically calculated, and the velocity potential in the mean water level (z = 0) satisfies the continuity equation and the kinematic bottom boundary condition. Wave generation and transformation are investigated when the triangular and rectangular shape of bottoms move periodically. The results of the simplified numerical method are compared with the results of previous analytical solutions and agree well with them. Stability of numerical results according to the calculation time interval (Δt) and the calculation wave number interval (Δk) was also investigated. It was found that the numerical results were appropriate when Δt ≤ T(period)/1000 and Δk ≤ π/100.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.90-95
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• 2001

현재까지 고주파수 진동해석에 가장 많이 쓰이는 방법은 통계적 에너지 해석법 (SEA)이다. 그러나 SEA는 많은 가정을 사용하고 있고 시간 및 공간 평균된 에너지 값을 사용하기 때문에 결과에서 알아낼 수 있는 정보가 제한된다. 이러한 단점을 극복하기 위하여 진동 전도 해석법(VCA)이나 파동 인텐시티기법 (WIA)등이 제안되었고, 기하음향학의 한 방법인 레이 추적 기법 (RTM)도 구조음향학에 적용하고 있다. 본 논문에서는 레이 추적 기법을 이용하여 오일러-베르누이 보 이론에 근거한 고정단-자유단 경계조건을 가지는 단일 곡보의 진동 해석을 수행하였다. 예제를 통한 해석 결과, 주파수가 높을수록, 또 감쇠가 클수록 더 정확한 결과를 예측할 수 있음을 관찰할 수 있었으며, 따라서 기존 해석법들의 가정에 적합하지 않은 구조물에 적용할 수 있는 장점이 있다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.18 no.3
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• pp.225-240
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• 2006

In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1287-1294
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory Both the divergence and flutter critical loads are calculated from the load-frequency corves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the subtangential parameter, mass ratio and spring parameter.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.1A
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• pp.117-132
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• 2006

The existing analytical solutions for rectangular plates with three edges clamped and the other free are derived based on nondimensional differential equation and their characteristics are analyzed. Since Timoshenko and Woinowsky-Krieger's method (1959) can give solutions for the case limited to the aspect ratio of the plates less than one, this method are proved to be impractical for the bending moment calculation of the plates under consideration. Horii and Moto's method(1968) are modified by adding stabilizing terms to suppress overflow in the matrix computation, from which the series solution with maximum 150 terms can be obtained. By use of the series solution the convergence of computed bending moments is tested. The modified method can be shown to calculate the deflection properties for the plates with wide range of aspect ratios, but the computed x moment at the corner points formed by the free edge and the clamped edges can not satisfy the boundary condition and the cause of problem is discussed in detail.