• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.279-283
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• 2004

Thermal postbuckling and vibration analyses of functionally graded plates (FG plates) are performed. The nonlinear finite element equation based on the first-order shear deformation plate theory is formulated for the FG plate. The von Karman strain-displacement relation is used to account for the thermal large deflection. The incremental method considering the effect of the initial deflection and the initial stress is adopted for temperature-dependent material properties of functionally graded materials. The numerical result shows characteristics of the thermal postbuckling and vibration of FG plates in the pre- and post- buckled regions.

• Coupled systems mechanics
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• v.11 no.5
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• pp.389-409
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• 2022

During the manufacture of FGM plates, defects such as porosities can appear. Those can change the entire behavior of these plates. This paper aims to investigate the free vibration characteristics of porous functionally graded (FG) plates resting on elastic foundations. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power-law formulation, and the Poisson ratio is held constant. Different types of porosity distribution rates are considered. To examine the accuracy of the present formulation, several comparison studies are investigated. Effects of variation of porosity distribution rate, foundation parameter, power-law index and thickness ratio on the fundamental frequency of plates have been investigated.

• Steel and Composite Structures
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• v.34 no.2
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• pp.215-226
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• 2020

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

• Steel and Composite Structures
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• v.18 no.1
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Journal of Mechanical Science and Technology
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• v.15 no.10
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• pp.1408-1416
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• 2001

It is very important to well understand the dynamic characteristics of damaged structures to successfully develop or to choose a most appropriate structural damage identification method (SDIM) as the means of non-destructive testing. In this pope., the dynamic equation of motion for damaged plates is derived by introducing a damage distribution function, which may characterize the effective state of structural damages. It is found that structural damages may induce the coupling between modal coordinates. The effects of damages on the vibration characteristics of a plate depending on their locations, sizes, and magnitudes are numerically investigated in a systematic way. The numerical investigations are also given to the effects of damage-induced modal coupling on the changes in vibration characteristics and to the minimum number of natural modes required to predict sufficiently accurate vibration characteristics of damaged plates.

• Journal of KSNVE
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• v.2 no.4
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• pp.305-315
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• 1992

In order to investigate the effects of layer-wise in-plane displacements on vibration and damping characteristics of composite laminated plates, the finite element method based on the generalized laminated plate theory(GLPT) has been formulated. Specific damping capacity of each mode was obtained by modal strain energy method. To see the effect of transverse shear on deformation, the strain energy of stress components was computed. The accuracy of this study was examined for the cylindrical bending vibration of cross-ply plate strip. The results were very accurate compared with 3-D solutions. The numerical results show that through-thickness variation of in-plane displacements has not so much influence on the natural frequency, but has a great influence on the damping of composite plates, especially on the damping of thick composite plates since the damping is affected by local behavior while the natural frequency is affected by global behavior.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.35-48
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• 1995

This paper presents new frequency results for elliptical and semi-elliptical Mindlin plates of various aspect ratios, thicknesses and boundary conditions. The results were obtained using the recently developed computerized Rayleigh-Ritz method for thick plate analysis. For simply supported elliptical plates, it is proposed that the penalty function method be used to enforce the condition of zero rotation of the midplane normal in the tangent plane to the plate boundary.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.8
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• pp.828-837
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• 2009

Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on elastic foundation(in a case of pasternak foundation or winkler foundation). And there are many machines in sub-structures of buildings and slabs of sub-structures are affected by vibration which they make. This paper deals with vibration of plates on elastic foundation. Machines on plates are considered as concentrated mass. This paper has the object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate with Concentrated Masses in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. The Winkler parameter is varied with 10, $10^2$, $10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0. And the Concentrated Mass is applied as P1, Pc, P2 respectively.

• Journal of KSNVE
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• v.7 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1899-1909
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• 1994

This work presents the experimental and FEM results for the free vibration of cantilevered, symmetrically and antisymmetrically laminated composite rectangular plates. The natural frequencies, mode shapes and contour plots of a number of CFRP, GFRP, DFRP-Aluminum, GFRP-Aluminum and DFRP-GFRP hybrid composite plates are experimentally obtained. Determination of Young's modulus and test procedures are described. The natural frequencies are determined for a wide range of parameters : e.g. , composite material constants, fiber angles and stacking sequences. Natural frequency and nondimensional frequency parameter results are compared with the finite element analysis and existing literatures. Agreement between experimental and calculated frequencies is excellent. The effects of varing the parameters upon the free vibration frequencies and mode shapes are discussed.