Closed-form solution for free vibration of piezoelectric coupled annular plates using Levinson plate theory

Abstract

Free vibration analysis of annular moderately thick plates integrated with piezoelectric layers is investigated in this study for different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Levinson plate theory (LPT). The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study the closed-form solution for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. To demonstrate the accuracy of the present solution, comparison studies is first carried out with the available data in the literature and then natural frequencies of the piezoelectric coupled annular plate are presented for different thickness-radius ratios, inner–outer radius ratios, thickness of piezoelectric, material of piezoelectric and boundary conditions. Present analytical model provides design reference for piezoelectric material application, such as sensors, actuators and ultrasonic motors.