Abstract
Three‐dimensional analysis of spherical or cylindrical transducers with axially or radially polarized piezoelectric ceramics is rather difficult because it needs a large number of classical elements to take into account the correct polarization. A new type of piezoelectric finite element has been developed in the ATILA code [J. N. Decarpigny et al., J. Acoust. Soc. Am. 78, 1499 (1985)] to obtain a good representation of the polarization. This paper describes these elements and analyzes the results (in air resonance modes, electrical characteristics, and mode shapes) obtained on some examples.
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