AN ACCURATE MATHEMATICAL STUDY ON THE FREE VIBRATION OF F UNCTIONALLY GRADED RECTANGULAR PLATES

A dynamic model of a functionally graded rectangular plate is presented in this paper. The material properties of the plate are considered to vary smoothly in the thickness direction. Employing a four variable displacement field, the equations of motion are derived via Hamilton’s principle and decoupled following an analytical procedure. Assuming levy-type boundary conditions, two decoupled equations are solved analytically in order to obtain the natural frequencies of the plate. The reliability and versatility of the results extracted from the presented fonnulation are verified, wl1icl1 induces some comparison studies for different cases (boundary conditions and geometric parameters). Some well-known behavior can be observed in either homogeneous or FG plates. On this basis, some results for the free vibration of FG rectangular plates with various boundary conditions are presented in order to show the advantages of the proposed formulation over some classical versions of first-order shear deformation plate theories in terms of accuracy and simplicity.

Keywords:

Free vibration , Functionally graded materials , Analytical procedure , Plates