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

Özet

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 deter-mine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction mod-ulus and the boundary conditions on the frequency parameters of thick plates sub-jected to free vibration. In the analysis, finite element method is used for spatial in-tegration. Finite element formulation of the equations of the thick plate theory is de-rived 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