Modeling and analysis of multilayer piezoelectric-elastic spherical transducers

An exact analytical model of multilayer piezoelectric-elastic spherical transducers is established in this article, and their dynamic characteristics are studied. Based on the linear theory of piezoelasticity, the dynamic analytical solution is derived in terms of Bessel functions, Lommel functions, Gamma functions, and Generalized Hypergeometric functions, and the electric impedance is obtained to determine the resonance frequencies. By proper selection of the layer number and geometric dimensions, the proposed model can approximately degrade into some special cases in the previous works, including single-layer piezoelectric spherical transducer, two-layer piezoelectric-elastic spherical transducer, and three-layer sandwiched piezoelectric-elastic-piezoelectric spherical transducer. Comparisons between the results of the proposed model and the ones of these special cases are also given and good agreements are found. Furthermore, parametric studies are conducted to discuss the effects of the key parameters on the dynamic characteristics of these special cases and a multilayer case, such as the first resonance and anti-resonance frequencies as well as the corresponding electromechanical coupling factor. This work contributes to an overall understanding of the dynamic characteristics of miniature piezoelectric hollow sphere transducers (BBs) and stacked piezoelectric spherical transducers. The developed model can be used to guide the design of the multilayer piezoelectric-elastic spherical transducers for promising applications in underwater acoustic detection, ultrasonic imaging, hydrophones, and nondestructive testing.