• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.401-411
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• 2001

This paper deals with the vibration analysis of the rectangular plates which are subjected to uniform in-plane stresses and supported on In-homogeneous Pasternak foundation. Two parametric foundation which Winkler foundation parameter and shear foundation parameter considered, is called by the Pasternak foundation. The values of Winkler foundation parameter of central and border zone of plate are chosen as k₁and k₂respectively, and the value of shear foundation is chosen as constant about all zone of plate. After composing global flexural stiffeness matrix, geometrical stiffeness matrix, mass matrix, and the stiffeness matrix of the Pasternak foundation, eigenvalue problems which are composed of these matrices are solved. The result shows that the shear foundation parameter must not be ignore when considering the stiffeness of foundation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.852-857
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• 2003

This paper has the object of investigating natural frequencies of thick plates on inhomogeneous Pasternak foundation by means of finite element method and providing kinematic design data lot mat of building structures. This analysis was applied for design of substructure on elastic foundation. Mat of building structure may be consisdered as a thick plate on elastic foundation. Recently, as size of building structure becomes larger, mat area of building structure also tend to become target and building structure is supported on inhomogeneous foundation. In this paper, vibration analysis or rectangular thick plate is done by use or serendipity finite element with 8 nodes by considering shearing strain of plate. The solutions of this paper are compared with existing solutions and finite element solutions with 4${\times}$4 meshes of this analysis are shown the error of maximum 0.083% about the existing solutions. It is shown that natrural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.711-714
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• 2005

This paper is for the vibration analysis of thick plate with concentrated mass on a inhomogeneous pasternak foundation. the thick rectangular plate resting on a inhomogeneous pasternak foundation is isotropic, homogeneous and composite with linearly elastic material. In order to analyize plat which is supported on inhomogeneous pasternak foundation, the value of winkler foundation parameter(WFP) of centural and border zone of plate are chosen as Kw1 and Kw2 respectively. The value of Kw1 and Kw2 can be changed as 0, 10, $10^2,\;10^3$ and the value of SFP(shear foundation parameter) also be changed 0, 5, 10, 15 respectively. Finally, In this paper, vibration of retangular plate on the inhomogeneous pasternak foundation, natural frequency of this plate with Concentrated Mass are calculated

• Journal of Korean Society of Steel Construction
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• v.13 no.1
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• pp.91-100
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• 2001

This paper is to analyze the stability of Timoshenko beam-column on Pasternak foundation, with the extensional and the rotational spring at center point of span by Finite Element Method. To verify this Finite Element Method, the results by the proposed method are compared with the existing solutionsof Timoshenko beam-column without the extensional and the rotational spring and the shear foundation. The dynamic stability regions are decided by the dynamic stability analysis of Timoshenko beam-column on Pasternak foundation with the extensional and the rotation spring at center point of span.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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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.

• Journal of Korean Society of Steel Construction
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• v.15 no.3
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• pp.291-298
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• 2003

Recently, as the size of buildings structure becomes large increases, their mat area of building structure is supported or by an inhomogeneous foundation. This paper presents a vibration analysis on thick plates subjected to in-plane force is presented in this paper. The rectangular plate is isotropic, homogeneous, and composed of a linearly elastic material. A vibration analysis of the rectangular thick plate iwas done by useing ofarectangular finite element with 8 nodes and 9 nodes. In this study, the foundation was idealized as a Pasternak foundation model. A Pasternak foundation haves a shear layer on Winkler's model, which idealizes the foundation as a vertical spring. In order tTo analysze the vibration of a plate supported on by an inhomogeneous Pasternak foundation, the value of the Winkler foundation parameter of the central and border zones of the plate awere chosen as WFP1 and WFP2. (fFigure 4.). The Winkler foundation parameter of WFP1 and WFP2 is varied from 0 to 10, $10^2$, and $10^3$ and the shear foundation parameters is were 0, 5, and 10. The ratio of the in-plane force to the critical load iwas applied as 0.4 to 0.8

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.12
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• pp.1296-1305
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• 2009

This paper has the object of investigating dynamic stability of stiffened tapered thick plate with concentrated mass on Pasternak foundation by means of finite element method and providing kinematic design data for mat of building structures. Finite element analysis of stiffened tapered thick 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 foundation parameter is varied with 10, 100, 1000 and the shear foundation parameter is 5, 10, concentrated mass is $0.25m_c$, $1.0m_c$, tapered ratio is 0.25, 0.5. The ratio of In-plane force to critical load is applied as $0.4\sigma_{cr},\;0.6\sigma_{cr},\;0.8\sigma_{cr}$ respectively. This paper analyzed varying tapered ratio.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.4
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• pp.281-289
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• 2003

Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on in-homogeneous 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 with concentrated masses on in-homogeneous foundation. Machines on plates are considered as concentrated masses. In-homogeneous foundation is considered as assigning $k_{w1}$ and $k_{w2}$ to Winkler foundation parameters of central region and side region of plate respectively, and foundation is idealized to use Pasternak foundation model which considered both of Winkler foundation parameter and shear foundation parameter. In this paper, applying Winkler foundation parameters which $k_{w1}$and $k_{w2}$ are 10, $10^2$, $10^3$ and shear foundation parameter which are 10, 20 respectively, first natural frequencies of thick plates with concentrated masses on in-homogeneous foundations are calculated.

• Geomechanics and Engineering
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• v.18 no.2
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• pp.161-178
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• 2019

In this research, a simple quasi 3D hyperbolic shear deformation model is employed for bending and dynamic behavior of functionally graded (FG) plates resting on visco-Pasternak foundations. The important feature of this theory is that, it includes the thickness stretching effect with considering only 4 unknowns, which less than what is used in the First Order Shear Deformation (FSDT) theory. The visco­Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The equations of motion for thick FG plates are obtained in the Hamilton principle. Analytical solutions for the bending and dynamic analysis are determined for simply supported plates resting on visco-Pasternak foundations. Some numerical results are presented to indicate the effects of material index, elastic foundation type, and damping coefficient of the foundation, on the bending and dynamic behavior of rectangular FG plates.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.8
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• pp.698-707
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• 2011

This paper is to analyze the stability of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass by finite element method. To verify this finite element method, the results of natural frequencies and buckling stresses by the proposed method are compared with the existing solutions. The dynamic instability regions are decided by the dynamic stability analysis of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass. The non-dimensional Winkler foundation parameter is applied as 100, 1000 and non-dimensional shear foundation parameter is applied as 5. The tapered ratios are applied as 0.25 and 1.0, the ratios of concentrated mass to plate mass as 0.25 and 1.0, and the ratio of in-plane force to critical load as 0.4. As the result of numerical analysis of the thick plate on inhomogeneous Pasternak foundation for $u{\times}v=300cm{\times}300cm$ and $a{\times}b=600cm{\times}600cm$, instability areas of the thick plate which has the larger rigidity of inner area are farther from ${\beta}$-axis and narrower than those which has the larger rigidity of outer area.