Model for Radial Modes in a Thin Piezoelectric Annular Array

Abstract

Piezoelectric arrays with different connectivities are widely used in actuators, transformers, and special ultrasonic transducers. In this study, the global matrix method is presented to describe the resonance radial modes in thin piezoelectric annular arrays with an arbitrary number of elements. Each annular element of the arrays is modeled as a three-port system with one electrical and two mechanical ports. The cored matrix model for radial modes, in a singular ring, is presented in the form of a translation matrix. The dynamic behavior of two annular arrays, a transformer and a Bessel transducer, is simulated assuming that the major surfaces of each element are stress-free, while the laterals are matched with neighbor elements. Thus, the inner and outer lateral surfaces of the system are loaded with an external medium. The simulated and experimental results are in good agreement when the thickness effects are neglected.