Exact analysis of radial vibration of functionally graded piezoelectric ring transducers resting on elastic foundation

An exact solution is obtained to analyze the electromechanical characteristics of functionally graded piezoelectric ring transducers in radial vibration. The material properties of piezoelectric ring transducers are assumed to be graded in power-law distribution form along the radial direction. The material inhomogeneity index of mass density can be different from that of the elastic, piezoelectric and dielectric constants. Analytical solution is obtained in terms of Bessel functions. The characteristic equations governing the resonant and anti-resonant frequencies are presented. Numerical results are depicted graphically to illustrate the effect of material inhomogeneity index and elastic foundation stiffness on the radial vibration characteristics, such as resonant/anti-resonant frequencies, effective electromechanical coupling factor and model shape.