• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.805-809
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• 2004

This paper is for the vibration analysis of thick plate with concentrated mass on a inhomogeneous pasternak foundation. The vibration of rectangular plate on the inhomogeneous pasternak foundation, natural frequency of this plate with Concentrated Mass are calculated A thick rectangular plate resting on a inhomogeneous pasternak foundation is isotropic, homogeneous and composite with linearly elastic material. In order to analysis plate which is supported on inhomogeneous pasternak foundation, the value of winkler foundation parameter(WFP) of centural and border zone of plate are chosen as WFP1 and WFP2 respectively. The value of WFP1 and WFP2 can be changed as 10, 10$^3$ and the value of SFP(shear foundation parameter) also be changed 5, 15 respectively.

• Advances in materials Research
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• 제5권4호
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• pp.245-261
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• 2016

Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a power-law form. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen's nonlocal elasticity theory. Navier's method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

• Structural Engineering and Mechanics
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• 제40권4호
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Coupled systems mechanics
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• 제10권1호
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• pp.61-77
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• 2021

The porosity of functionally graded materials (FGM) can affect the static and dynamic behavior of plates, which is important to take this aspect into account when analyzing such structures. The present work aims to study the effect of the distribution shape of porosity on the free vibration response of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is expanded to study the influence of the distribution shape of porosity on the free vibration behavior of FG plates. The findings showed that the distribution shape of porosity significantly influences the free vibration behavior of thick rectangular FG plates for small values of Winkler-Pasternak elastic foundation parameters.

• Structural Engineering and Mechanics
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• 제60권4호
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• pp.615-631
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• 2016

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

• 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.

• Steel and Composite Structures
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• 제14권1호
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• 한국전산구조공학회논문집
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• 제15권2호
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• pp.367-377
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• 2002

이 논문은 탄성지반 위에 놓인 낮은 아치의 자유진동에 관한 연구이다. Pasternak가 제안한 두 개의 매개변수로 표현되는 지반모형을 채택하여 대상아치의 자유진동을 지배하는 미분방정식을 유도하였다. 양단회전 및 양단고정의 단부 조건을 갖는 두 종류의 아치선형을 유도된 지배방정식에 적용하여 Galerkin method로 해석함으로써 최저차 대칭 및 역대칭 고유진동수 방정식을 산출하였다 아치높이, Winkler지반계수 및 전단지반계수가 고유진동수에 미치는 영향을 분석하였으며, 아치선형이 고유진동수에 미치는 영향을 분석하였다.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.219-232
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• 2018

This paper deals with the static bending of various types of FGM sandwich plates resting on two-parameter elastic foundations in hygrothermal environment. The elastic foundation is modeled as Pasternak's type, which can be either isotropic or orthotropic and as a special case, it converges to Winkler's foundation if the shear layer is neglected. The present FGM sandwich plate is assumed to be made of a fully ceramic core layer sandwiched by metal/ceramic FGM coats. The governing equations are derived from principle of virtual displacements based on a shear and normal deformations plate theory. The present theory takes into account both shear and normal strains effects, thus it predicts results more accurate than the shear deformation plate theories. The results obtained by the shear and normal deformation theory are compared with those available in the literature and also with those obtained by other shear deformation theories. It is concluded that the present results are slightly deviated from other results because the normal deformation effect is taken into account. Numerical results are presented to show the effects of the different parameters, such as side-to-thickness ratio, foundation parameters, aspect ratio, temperature, moisture, power law index and core thickness on the stresses and displacements of the FG sandwich plates.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.467-474
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• 2001

This paper is for the buckling and vibration analysis of thick plate with concentrated mass on a inhomogeneous pasternak foundation. A thick rectangular plate resting on a inhomogeneous pasternak foundation is isotropic, homogeneous and composite with linearly elastic material. In order to analyize plate which is supported on inhomogeneous pasternak foundation, the value of winkler foundation parameter(WFP) of centural and border zone of plate are chosen as Kwl and Kw2 respectively. The value of Kwl and Kw2 can be changed as 0, 10, 10 /sup 2/, 10 / sup 3/ and the value of SFP(shear foundation parameter) also be changed 0, 5, 10, 15 respectively. Finally, In this paper, buckling stress of rectangular plate on the inhomogeneous pasternak foundation, natural frequency of this plate with or without uniform in-plane axial stresses are calculated