• Structural Engineering and Mechanics
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• 제70권1호
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• pp.97-112
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• 2019

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.

• 한국소음진동공학회논문집
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• 제18권6호
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• pp.681-689
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• 2008

This paper is concerned with the free vibration analysis of a circular plate with an eccentric circular hole by the Independent coordinate coupling method(ICCM). It was proved in the previous study that the ICCM can accurately predict the natural frequencies and mode shapes of the annular plates and can also be used for the free vibration analysis of the simply-supported circular plate with an eccentric circular hole. In this study, the clamped and free boundary conditions were considered for the circular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of circular plate with an eccentric hole compared to the finite element method.

• Coupled systems mechanics
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• 제11권4호
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• pp.357-371
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• 2022

This paper presents a parametric study on the free vibration analysis of a functionally graded material (FGM) circular plate with non-uniform thickness resting on a variable Pasternak elastic foundation. The mechanical properties of the material vary in the transverse direction through the thickness of the plate according to the power-law distribution to represent the constituent components. The equation of motion of the circular plate has been carried out based on the classical plate theory (CPT), and the differential quadrature method (DQM) is employed to solve the governing equations as a semi-analytical method. The grid points are chosen based on Chebyshev-Gauss-Lobatto distribution to achieve acceptable convergence and better accuracy. The influence of geometric parameters, variable elastic foundation, and functionally graded variation for clamped and simply supported boundary conditions on the first three natural frequencies are investigated. Comparisons of results with similar studies in the literature have been presented and two-dimensional mode shapes for particular plates have been plotted to illustrate the effect of variable thickness profile.

• Structural Engineering and Mechanics
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• 제29권3호
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• pp.279-288
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• 2008

In the present study, the discrete singular convolution (DSC) method is developed for buckling analysis of columns and thin plates having different geometries. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The results obtained by DSC method were compared with those obtained by the other numerical and analytical methods.

• Structural Engineering and Mechanics
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• 제29권2호
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• pp.237-240
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• 2008

• 한국전산구조공학회논문집
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• 제17권2호
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• pp.119-129
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• 2004

3차원 해석법을 이용하여 반경방향으로 비선형적 두께 변분을 가진 두꺼운 원형판과 환형판의 고유진동수를 결정하였다. 수학적으로 2차원적인 전통적 판 이론과는 달리 본 연구에서는 3차원적 등 탄성방정식을 근간으로 하였다. 반경방향, 두께방향, 원주방향으로의 변위 성분인 u/sub s/, u/sub z/, u/sub θ/를 시간에 대해서는 정현적으로, θ에 대해서는 주기적으로, s와 z방향으로는 대수 다항식의 형태로 취하였다. 판의 위치(변형률) 에너지와 운동 에너지를 정식화하고, 리츠법을 이용하여 고유치 문제를 해결하였으며, 진동수의 최소화과정을 통해 엄밀해에 대해서 상위경계치의 진동수를 구하였다. 다항식의 차수를 증가시키면 진동수는 엄밀해에 수렴하게 된다. 판의 최하위 5개의 진동수에 대한 유효숫자 4자리까지의 수렴성 연구가 이루어졌다. 수치결과로 두께가 일정하거나, 선형적 또는 2차 곡선적 변분을 갖는 자유경계의 두꺼운 원형판과 환형판의 무차원 진동수를 제공하였다. 또한 이미 발표된 2차원적인 박판이론에 의한 결과와 본 연구의 3차원 해석에 의한 결과를 서로 비교하였다.

• 한국신재생에너지학회:학술대회논문집
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• 한국신재생에너지학회 2005년도 춘계학술대회
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• pp.534-537
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• 2005

Free Vibration Analysis using Non-dimensional Dynamic Influence Function (NDIF) is extended to arbitrarily shaped plates including polygonal plates. Since the corners of polygonal plates have indefinite normal directions and additional boundary conditions related to a twisting moment at a corner along with moment and shear force zero conditions, it is not easy to apply the NDIF method to polygonal plates wi th the free boundary condition. Moreover, owing to the fact that the local polar coordinate system, which has been introduced for free plates with smoothly varying edges, cannot be employed for the straight edges of the polygonal plates, a new coordinate system is required for the polygonal plates. These problems are solved by developing the new method of modifying a corner into a circular arc and setting the normal direction at the corner to an average value of normal direct ions of two edges adjacent to the corner. Some case studies for plates with various shapes show that the proposed method gives credible natural frequencies and mode shapes for various polygons that agree well with those by an exact method or FEM (ANSYS).

• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Steel and Composite Structures
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• 제48권3호
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Nuclear Engineering and Technology
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• 제41권3호
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• pp.355-364
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• 2009

Circular plates with holes are extensively used in mechanical components. The existence of a hole in a circular plate results in a significant change in the natural frequencies and mode shapes of the structure. Especially if the hole is located eccentrically, the vibration behavior of these structures is expected to deviate significantly from that of a plate with a concentric hole. In addition, if the plate is in contact with or submerged in fluid, the situation is more complex. Therefore, in this study, an analytical method to determine the modal characteristics of a plate submerged in fluid is developed based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method and is verified by the finite element analysis using a commercial program. Also, the relationship between parameter variations and vibration modes is investigated. These results can be used as guidance for the modal analysis and damage detection of a circular plate with a hole.