Donald Ricketts

Multi-layered polymer hydrophone array

A piezoelectric polymer (PVDF) hydrophone array consists of multiple layers disposed symmetrically about a stiffener layer. The stiffener layer prevents flexural modes in the operating frequency band and provides a mounting structure for acceleration noise cancellation. The piezoelectric polymer layers are attached to the stiffener layer either directly or through intervening layers which provide mechanical vibration isolation of the polymer and stiffener layers.

The frequency of flexural vibration of completely free composite piezoelectric polymer plates

The frequency expression for flexural vibrations of the completely free composite piezoelectric polymer plate given in an earlier paper [J. Acoust. Soc. Am. 77, 1939–1945 (1985)] for all modes of the type p/q (p, q=2,3,4,...) is extended to cover all modes of this type for p, q=0,1,2,..., where p and q are the number of nodal lines in the coordinate directions x1 and x2, respectively. Because of the stiffening effect of electrodes deposited on the polymer surface, the expressions for the flexural and twisting rigidities of the composite plate given in the earlier paper for 2n layers are rewritten with the electrodes treated as layers separate from the polymer. Expressions are also given for the rigidities of the composite plate for an odd number of layers, a case not considered in the earlier paper. The frequencies of several modes are computed for a completely free composite piezoelectric polymer plate, a configuration which has application to hydrostatic polymer hydrophones.

Electroacoustic sensitivity of composite piezoelectric polymer cylinders

The low‐frequency electroacoustic sensitivity of piezoelectric polyvinylidene fluoride (PVF2) film attached to a cylindrical tube substrate is derived for three boundary conditions. Sensitivity expressions are developed for both the PVF2 film attached to the inside or outside surface of the tube for each of the three boundary conditions. Experimental verification of the theory has been obtained for the capped composite polymer cylinder, with close agreement between the theoretical and measured sensitivities.

Model for a piezoelectric polymer flexural plate hydrophone

A mathematical model of the piezoelectric polymer flexural plate hydrophone is presented, with application to sheets of polymer attached to air‐backed rectangular flexural plates. Expressions are given for the low‐frequency electroacoustic sensitivity, as well as for the evaluation of hydrophone mechanical behavior under hydrostatic loading. Numerical results are presented for the supported plate and for the special case of a supported beam. The analytic results reveal that the selection criterion for the substrate plate should be its strength‐to‐elastic modulus ratio, in order to maximize the product of hydrophone sensitivity and maximum operating pressure. The theoretical model is applied to a plastic flexural plate polymer hydrophone, which results in close agreement between the predicted and measured sensitivities.

Transverse vibrations of composite piezoelectric polymer plates

Free transverse vibrations of the multilayered rectangular plate are considered. The composite plate consists of 2n orthotropic layers symmetrically located about the midplane, where the central (n and n+1) layers are piezoelectric polymer. Using the Rayleigh method, closed formulas are obtained for the frequencies of flexural vibration. A generalized frequency expression is presented in terms of definite integrals containing the characteristic functions. Formulas for evaluating these integrals for common types of boundary conditions are available in the literature. In particular, an expression is derived for the resonance frequencies of the completely free composite piezoelectric polymer plate.

Evaluation of the property coefficients of piezoelectric polymers

Analytical models are presented for evaluating the property coefficients of thick‐film piezoelectric polymers. In particular, these models facilitate the evaluation of the complex elastic compliance coefficients ŝ1′1′D, ŝ12D, ŝ22D, ŝ33D, and ŝ66D from the measured set of quantities {fm,fl,fn,Al,An}, where fm is the resonance frequency of the test specimen fl<fm<fn and Al and An are the relative amplitudes at the selected frequencies fl and fn. Impact excitation of the test samples, a vibration sensor, and a FFT‐based spectrum analyzer are used to measure these quantities. In addition, a model is presented for evaluating the complex electromechanical coupling factor k31 from the measured value of the transfer function of the length expander polymer bar with divided electrodes. Experimental results were obtained on PVF2 samples made by Raytheon Research Division, and the analytical models were used to evaluate the property coefficients of these samples. The results of these evaluations for ŝ11D, ŝ1′1′D, ŝ1...

Performance prediction models for piezoelectric polymer hydrophones

Mathematical models of several types of piezoelectric polymer hydrophones have been developed which facilitate an evaluation of their low‐frequency electroacoustic sensitivity as well as maximum operating pressure (Pmax). The flexural rectangular plate and disk and also cylindrical hydrophone elements have been investigated for various boundary conditions, where in each case the polymer film is attached to a substrate which establishes the geometric configuration of the hydrophone. The theoretical results for flexural elements together with practical design considerations indicate that matching of the elastic moduli of the polymer and the selected substrate material yields better hydrophone sensitivity. But to maximize the product of sensitivity and Pmax without pressure compensation, the selection of the substrate material should be based upon maximizing the ratio of substrate mechanical strength to elastic modulus. Experimental verification of the theoretical models has been obtained for both the bender...

Evaluation of the complex coefficients ŝ33H, d̂33, and μ̂33T of length expander magnetostrictive rods

An analytical model is presented for evaluating the effective complex material coefficients of length expander piezomagnetic rods with magnetic field in the direction of wave propagation. In particular, the model facilitates the evaluation of complex ŝ33H, k33, μ33, and d33 from the measured set of quantities [fRI,QMI, fRE,QME,Zex, fex], where the superscripts I and E denote the ac open‐circuit and short‐circuit conditions, respectively. Thus fRI and QMI are the measured ac open‐circuit resonance frequency and mechanical storage factor; likewise for fRE and QME. Here, Zex is the measured value of the electrical impedance at the frequency fex. An impact testing technique [J. Acoust. Soc. Am. Suppl. 1 67, S32 (1980)] is used to measure the resonance frequencies and mechanical storage factors of the free‐free magnetostrictive rod test specimen for the two electric boundary conditions. Experimental results are presented for ŝ33H, d33, and μ33T of grain‐oriented Terfenol‐D rods for several levels of magne...

Evaluation of the complex coefficient ŝD33 of thlck film piezoelectric polymers

A model for evaluating ŝD33 is presented using an impact testing technique [J. Acoust. Soc. Am. Suppl. 1 67, S32 (1980)]. In the form of a consolidated bare ring stack, the piezoelectric polymer (PYF2) test specimen is sandwiched between two identical loading masses. A threaded tie rod passes through the center of the entire assembly and is fastened at each end by means of a nut. This arrangement facilitates evaluating ŝD33 as a function of frequency and compressive stress. By impact testing this composite longitudinal vibrator, its resonance frequency (fR) and mechanical storage factor (QM) may be measured. From these measured quantities and the mathematical model of the test resonator, the complex elastic compliance coefficient ŝD33 may be evaluated. The expressions for evaluating the real and imaginary parts of ŝD33 are given. Experimental results obtained at room temperature are presented for ŝD33 versus compressive prestress at two nominal audio frequencies.

Reply to ‘‘Comments on ‘Transverse vibrations of composite piezoelectric polymer plates’ ’’ [J. Acoust. Soc. Am. 79, 1181 (1986)]

The author takes this opportunity to reply to Laura and Gelos [J. Acoust. Soc. Am. 79, 1181 (1986)] and to express his appreciation for their comments. He completes the orthogonal set of characteristic functions φi given in his paper and obtains a single‐term Rayleigh solution for the first six modes of the completely free composite piezoelectric polymer plate. The accuracy of these results for the case of an isotropic square plate is evaluated by direct comparison to the 36‐term Rayleigh–Ritz solution obtained by Leissa [J. Sound Vib. 31, 257–293 (1973)].