Abstracto

FREE VIBRATION ANALYSIS OF THIN ISOTROPIC RECTANGULAR PLATE

Prof. Ajay S. Patil

For free vibration response of rectangular plate, Navier’s analytical solution is available only for all edges simply supported (SSSS) plate. But for plate with different boundary conditions such as plate with all edges clamped (CCCC), plate with boundary conditions such as CCCF, CCFF and CFFF solutions are not available. In this paper, an available Modified Discrete Kirchhoff Quadrilateral (MDKQ) element is developed based on Classical Plate Theory (CPT) using discrete Kirchhoff technique. Earlier it is used only for static analysis of plate and no attempt is made to use it for free vibration response. The performance of the developed finite element formulation is assessed for free vibration response of thin isotropic rectangular plate with various boundary conditions and different aspect ratios. A computer program has been developed in FORTRAN using MDKQ interpolation functions for free vibration analysis of thin isotropic rectangular plate. The developed MDKQ element has 3 degrees of freedom at each node. Hamilton’s principle is used to formulate the stiffness and consistent mass matrices. It is observed that results of MDKQ element are quite close to the approximate analytical and finite element solutions available in the literature