Free vibration analysis of piezoelectric coupled thin and thick annular plate

This paper presents the free vibration analysis of piezoelectric coupled annular plates using the Kirchhoff and Mindlin plate models. The distribution of electric potential along the thickness direction in the piezoelectric layer is simulated by a sinusoidal function such that the Maxwell static electricity equation is satisfied. The analytical solutions are derived and validated by comparing the resonant frequencies and mode shapes of the piezoelectric coupled annular plates with those obtained by finite element (FE) analysis. Mindlin model provides better solutions than those from Kirchhoff model and the deviation from FE results is larger for higher resonant frequencies. The piezoelectric layer increases the resonant frequencies, being more significant for thicker layers. The effect is smaller for higher modes and for smaller radius to thickness ratio of the plate. The analytical solutions and findings contribute towards a simplified model for the parametric study and understanding of vibration of piezoelectric-coupled annular plate, relevant to the design of ultrasonic motor.