Vibration analysis of FG annular sector in moderately thick plates with two piezoelectric layers

Abstract

Free vibration of functionally graded (FG) annular sector plates embedded with two piezoelectric layers is studied with a generalized differential quadrature (GDQ) method. Based on the first-order shear deformation (FSD) plate theory and Hamilton’s principle with parameters satisfying Maxwell’s electrostatics equation in the piezoelectric layers, governing equations of motion are developed. Both open and closed circuit (shortly connected) boundary conditions on the piezoelectric surfaces, which are respective conditions for sensors and actuators, are accounted for. It is observed that the open circuit condition gives higher natural frequencies than a shortly connected condition. For the simulation of the potential electric function in piezoelectric layers, a sinusoidal function in the transverse direction is considered. It is assumed that properties of the FG material (FGM) change continuously through the thickness according to a power distribution law. The fast rate convergence and accuracy of the GDQ method with a small number of grid points are demonstrated through some numerical examples. With various combinations of free, clamped, and simply supported boundary conditions, the effects of the thicknesses of piezoelectric layers and host plate, power law index of FGMs, and plate geometrical parameters (e.g., angle and radii of annular sector) on the in-plane and out-of-plane natural frequencies for different FG and piezoelectric materials are also studied. Results can be used to predict the behaviors of FG and piezoelectric materials in mechanical systems.