Nonuniform piezoelectric circular plate flexural transducers with underwater applications

An analytical treatment is presented for circular flexural plate transducers that have nonuniform electromechanically active-passive mechanical systems with particular interest in underwater applications. The analysis is made using the energy method that was previously applied to calculating parameters of uniform fully active (bimorph) circular plate transducers [B. S. Aronov, J. Acoust. Soc. Am. 118(2), 627-637 (2005)]. It is shown that the vibration mode shapes remain sufficiently similar to those for uniform plates for a large range of relative dimensions of active and passive laminates of radially nonuniform mechanical systems, and they may be used for calculating transducer parameters. Therefore the transducers can be considered as having a single degree of freedom, and their operational characteristics can be determined using the same technique as previously used for uniform plates. Dependences of the resonance frequencies, effective coupling coefficients, and parameters of the equivalent electromechanical circuit on relative dimensions of active and passive laminates for several combinations of the active and passive materials are presented and compared with those parameters of uniform plates having the same overall dimensions. The results of experimental verification are in good agreement with theoretical predictions.