Research Articles | Challenge Journal of Structural Mechanics

Eigenvector and eigenvalue analysis of thick plates resting on elastic foundation with first order finite element

Yaprak Itır Özdemir


DOI: https://doi.org/10.20528/cjsmec.2018.02.004

Abstract


The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin’s theory with first 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 first order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 4-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 4-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, 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.


Keywords


parametric free vibration analysis; thick plate; Mindlin’s theory; first order finite element; Winkler foundation

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References


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