Vibration characteristics of functionally graded piezoelectric cylindrical transducers

An exact solution is developed for the radial vibration characteristics of functionally graded piezoelectric cylindrical transducers. The material properties, such as mass density, elastic, piezoelectric and dielectric constants, are assumed to be the power-law functions of radial position. The material nonhomogeneity index of mass density can be different from that of elastic, piezoelectric and dielectric constants. General solutions are obtained in terms of Bessel functions. The characteristics equations for the resonant and anti-resonant frequencies are derived by employing the obtained general solutions and the boundary conditions. The illustrative examples show that the vibration characteristics of functionally graded piezoelectric cylindrical transducers can be tuned by adjusting the material nonhomogeneity index.