Effects of circumferential stress on tangentially polarized piezoelectric cylinders.

This paper investigates the dependence of the electromechanical properties of the tangential polarized (stripe-electroded) cylindrical piezoelements made of the hard (PZT-4 like) and soft (PZT-5A like) ceramics on the compressive circumferential stress produced by hydrostatic pressure. Results are presented for the relative change of the effective dielectric constants, elastic constants, coupling coefficients, and piezoelectric moduli. The sensitivity of dielectric constant and piezoelectric modulus to the compressive stress is shown to be less than radially polarized ceramic.

Increasing piezoelectric effect in radially polarized soft piezoelectric cylinders by pressure treating and its practical applications.

Subjecting soft piezoelectric ceramics such as lead zirconate titanate (PZT)-5 to uniaxial stress in a direction perpendicular to the principal polarization axis is known to increase its transverse piezoelectric modulus [Krueger, J. Acoust. Soc. Am. 43 (3), 583-559 (1968)], however, practical transducer applications of this effect remain undeveloped. This study explores uniaxial pressure-treatment to develop experimental methods to realize practical pressure treatment, to use dynamic measurements of the electromechanical coupling coefficient k32, piezoelectric modulus, and dielectric constants, and to enhance piezoelectric properties and performance of underwater acoustic cylindrical transducer designs. The results of axial pressure treatment on parameters of the cylinders are shown to increase the coupling coefficient by about 20% and remained stable. The applicability of using pressure treated cylinders in transducer designs is investigated. The performance was analyzed under one-dimensional circumferential static compression and under the hydrostatic compression. When the improved piezoelectric cylinders are used in air-backed transducer designs, the benefit is only useful at shallow depths as it is observed that when subjected to increased hydrostatic pressure, the corresponding induced circumferential stress reduces the piezoelectric properties, namely, the coupling coefficient, to approximately its original pre-treated value. However, when the improved cylinders are used in transducers of the pressure-equalized design, such as liquid filled or free-flooded, the increase in coupling coefficient remains stable with environmental hydrostatic pressure.

Piezoelectric cylindrical discs and solid rods: Dependence of the resonance frequencies and effective coupling coefficients on aspect ratio.

Dependencies of the resonance frequencies and effective coupling coefficients for solid circular cylindrical piezoelements (discs) of finite size are considered as a function of their height-to-diameter aspect ratios, h/2a. At aspect ratios in the range of approximately 0.5 < h/2a < 1.5 the piezoelements are treated analytically, as a two degree-of-freedom coupled system by applying the coupled mode theory approach [Aronov, Bachand, and Brown, J. Acoust. Soc. Am. 126(6), 2983-2990 (2009)]. Results are presented as plots of resonance frequencies and effective coupling coefficients vs aspect ratios. Experimental verification showed good agreement with the analytical predictions and allowed sufficiently reliable characterization of the trends of parameters in the range of aspect ratios, for which the analytical treatment could not be applied. The equivalent parameters that characterize energy relations in the course of coupled vibration are determined, and the equivalent electromechanical circuit is introduced for calculating frequency response of the transducers.

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.

Piezoelectric circular ring flexural transducers.

An analytical treatment of the piezoelectric ceramic complete ring transducer undergoing flexural vibrations is presented. Conditions for the electromechanical excitation of the flexural vibrations are discussed and it is shown that the fundamental mode of the flexural vibration of a complete ring can be considered as sufficiently dominant over a broad frequency range. Hence, the one-dimensional equivalent electromechanical circuit representation of the transducer is applicable and all the parameters of the equivalent circuit are determined. Possibilities to optimize the effective coupling coefficient of the transducer by changing the extent of the electrodes on the piezoelectric body are considered. It is shown that for effective operation of the flexural ring transducer as a low frequency hydroacoustic projector the opposing quadrants (or three quadrants in case of a planar array configuration) have to be covered with baffles. The radiation impedance and directional factors of the transducers with baffles are considered. Limitations of the acoustical power radiated by the transducers are discussed.

Piezoelectric slotted ring transducer.

Analytical treatment of a slotted piezoelectric ceramic ring transducer vibrating in flexure is presented. The mode shape of the slotted ring vibration is determined, and parameters of the equivalent electromechanical circuit of the transducer are calculated. Possibilities to optimize the effective electromechanical coupling coefficient of the transducer by combining active and passive materials are considered. Acoustic loading for typical projectors made from slotted rings is estimated. Challenges in implementing the slotted ring transducers in terms of depth limitation and radiated power are discussed.

Analytical modeling of piezoelectric ceramic transducers based on coupled vibration analysis with application to rectangular thickness poled plates.

The energy method for analyzing piezoelectric ceramic transducers [B. S. Aronov, J. Acoust. Soc. Am. 117, 210-220 (2005)] is applied to the treatment of transducers with mechanical systems that can be considered as two-dimensional. Analysis is made following the general outline of the theory of coupled vibration in two degrees-of-freedom systems and its extension in calculating the resonance frequencies of elastic bodies, as suggested by Giebe and Blechschmidt [Ann. Physik, Ser. 5 18, 417-485 (1933)]. The approach to the problem is illustrated with examples of piezoceramic rectangular thickness poled plates. The resonance frequencies and effective coupling coefficients are presented as functions of the plates' aspect ratio.

On the dynamic measurement of constants of piezoelectric single-crystal materials.

An error in the estimation of piezoelectric material properties can arise when applying the common measurement procedures in the IEEE Standard to determining constants of piezoelectric materials with exceptionally high coupling coefficients, in particular, single-crystal materials. The probable sources of inaccuracy in the resonance-antiresonance method, when applied to bar samples made of single crystals are considered. An additional method of dynamic measurements that helps to avoid the shortcomings of the resonance- antiresonance method is proposed, and its application is illustrated with examples of measurement of single-crystal piezoelements of different compositions.