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Eigenvalue Analysis of Mindlin Plates Resting on Elastic Foundation

Yaprak Itır Özdemir


The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency parameters of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates as free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers designing of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can effectively be used in the free vibration analysis of thick plates. It is also concluded that, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio. 

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A. C. Ugural, Stresses in Plates and Shells, McGraw-Hill, New York, (1981).

R. M. Grice, R. J. Pinnington, Analysis of the flexural vibration of a thin-plate box using a combination of finite element analysis and analytical impedances, J. Sound Vib., 249(3), 499-527, (2002).

T. S. Lok, Q. H. Cheng, Free and forced vibration of simply supported, orthotropic sandwich panel, Comput. Struct., 79(3), 301-312, (2001).

W. J. Si, K. Y. Lam, S. W. Gang, Vibration analysis of rectangular plates with one or more guided edges via bicubic B-spline method, Shock Vib., 12(5), (2005).

Y. Ayvaz, A. Durmuş, Earthquake analysis of simply supported reinforced concrete slabs, J. Sound Vib., 187(3), 531-539, (1995).

E. Hinton, and HC. Huang, A Family of Quadrilateral Mindlin Plate Element with Substitute Shear Strain Fields, Computer and Structures, 23(3), 409-431, (1986).

O. C. Zienkiewich, R. L. Taylor, and J. M. Too, Reduced integration technique in general analysis of plates and shells, Int. J. for Numerical Methods in Engineering, 3, 275-290, (1971).

P. G. Bergan, and X. Wang, Quadrilateral Plate Bending Elements with Shear Deformations, Comput. Struct., 19(1-2), 25-34, (1984).

T. A. Ozkul and U. Ture, The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem, Thin-Walled Structures, 42, 1405-1430, (2004).

T. J. R. Hughes, R. L. Taylor, and W. Kalcjai, Simple and efficient element for plate bending, Int. J. for Numerical Methods in Engineering, 11, 1529-1543, (1977).

Y. I. Özdemir, S. Bekiroğlu, and Y. Ayvaz, Shear locking-free analysis of thick plates using Mindlin’s theory, Struct. Eng. Mech. 27(3), 311-331, (2007).

K. K. Raju, E. Hinton, Natural frequencies and modes of rhombic Mindlin plates, Earhq. Eng. Struct. Dyn., 8, 55-62, (1980).

Y. I. Özdemir, Y. Ayvaz, Shear Locking-Free Earthquake Analysis of Thick and Thin Plates Using Mindlin’s Theory, Struct. Eng. Mech. 33(3), 373-385, (2009).

R. D. Cook, D. S. Malkus, and E. P. Michael, Concepts and Applications of Finite Element Analysis. John Wiley & Sons, Inc., Canada, (1989).

K. J. Bathe, Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey, (1996).

W. Weaver, and P. R. Johnston, Finite elements for structural analysis, Prentice Hall, Englewood Cliffs; New Jersey, (1984).

Y. I. Özdemir, Development of a higher order finite element on a Winkler foundation, Finite Elem. Anal. Des., 48, 1400-1408, (2012).

K. Özgan, and A. T. Daloglu, Free vibration analysis of thick plates resting on Winkler elastic foundation, Challenge J. Struct. Mech., 1(2), 78-83, (2015).


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