Free vibration analysis of shear-induced flexural vibration of FGPM annular plate using Generalized Differential Quadrature method

This work deals with free vibration analysis of functionally graded piezoelectric (FGPM) annular plate excited using the shear effect. The shear piezoelectric coupling coefficient is higher than other piezoelectric coupling coefficients for longitudinal and lateral deformation. This makes it more attractive for engineering applications. A modified Mindlin plate theory is employed where the electric potential is assumed to have a sinusoidal variation through the thickness direction. Material constants are assumed to have a power law variation across the thickness. Theoretical formulations are derived by using Hamilton's principle. The available equations of motion are then solved using the Generalized Differential Quadrature (GDQ) method to obtain the natural frequencies of the FGPM annular plate. The accuracy of the method is validated by comparing the results with the previous study for the reduced case of isotropic plate. As there are no published work to validate the results therefore the results obtain by finite element modeling using COMSOL (version 4.2) software are used for validation. It is found that results obtained by proposed formulation are in good agreement with the results obtained by COMSOL software. The effect of plate thickness, volume fraction indices, diameter ratio and boundary conditions on natural frequencies are also reported.