Analysis of eigenfrequencies in piezoelectric transducers using the finite element method

Analysis of piezoelectric transducers is often based on one-dimensional methods such as equivalent circuits and transmission line models. This implies that the vibrational pattern is presumed rather than found by the analysis. The presumptions are valid only for simple geometries such as thin plates. The finite element method can determine the nature of the vibrations and is applicable to any geometry. Therefore it is a valuable supplement to the traditional methods for design of new transducer types. Computer programs for analysis of axisymmetric transducers, which include the complete set of piezoelectric equations have been developed. They can find eigenfrequencies for undamped transducers and make forced response analysis for transducers with internal and radiation damping. Super element technique is employed to model the transducer backing in an efficient way. Examples ranging from a freely vibrating disk to a real focused transducer with a conical backing are presented.