Computation of the Vibrational Modes for Piezoelectric Array Transducers Using a Mixed Finite Element-Perturbation Method

High resolution sonars and many acoustical imaging de- vices are using arrays of parallelepipedic ceramic transducers that may or may not be associated withh/4 matching layers. However, the cor- responding ceramics often exhibit parasitic modes (due to their finite dimensions), and even for the fundamental mode, there is no analyti- cal method yielding accurate prediction of the resonance frequency and of the mode coupling coefficient. A three-dimensional finite element method able to compute those elements and the correspond- ing vibration patterns has been developed. There, piezoelectricity is introduced by a perturbation technique which reduces core size re- quirements and computation costs drastically. Furthermore, com- parisons with experimental results in the special nonanalytical case of a PZT4 20-mm side cube demonstrate that the resonance and antiresonance frequencies are predicted to within a few percent of error in spite of the high coupling coefficient of the ceramic. It ap- pears that the error is due mostly to the size of the finite elements and not to the perturbation approximation. Computation and ex- perimental results obtained with other arrays used in the lab which incorporate h/4 matching layers are discussed; good agreement is shown again.