Response of bare 1-3 piezocomposite array to localized electrical excitation

The theoretical response of a 1-3 piezocomposite plate submitted to localized electrical excitation was studied with the theory of guided waves. The theoretical modeling was based on the global matrix method, and the piezocomposite material was considered as a homogeneous medium. To validate the theoretical results, experimental displacement measurements were performed with an interferometric probe on two piezocomposite plates, one with a single element and one with an array of electrodes. The measured response on the single-element plate was mainly supported by the S0 and S3 modes of the plate. Homogenization limits of the composite in terms of frequency and wave number are defined on the basis of data from this sample. Within these limits, the piezocomposite material operates as a homogeneous medium, and comparison between theoretical and experimental results allows the equivalent electroacoustic parameters to be evaluated. A second sample was measured to study the effects of the electrode array on the electroacoustic response of the plate. Two kinds of electrical excitation were studied.     

Single-element ultrasonic transducer modeling using a hybrid FD–PSTD method

In a recent publication [E. Filoux, S. Callé, D. Certon, M. Lethiecq, F. Levassort, Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods, J. Acoust. Soc. Am. 123 (6) (2008) 4165–4173], a new finite-difference/pseudospectral time-domain (FD–PSTD) algorithm was presented and used to model the generation of acoustic waves by a piezoelectric resonator and their propagation in the structure and the surrounding water. In this paper, the model has been extended to simulate the two-dimensional behaviour of a complete single-element transducer, composed of the resonator, a backing and a front matching layer. This further version of the model takes into account the mechanical loss in materials, and enables the calculation of electrical impedance, which is a characteristic of high interest to optimize the performance of ultrasonic transducers. The impedance curves of a PZT [URL: http://www.ferroperm-piezo.com (last viewed 04/2008); B. Jaffe, R.S. Roth, S. Marzullo, Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics, J. Appl. Phys. 25 (1954) 809–810] plate-based high-frequency transducer, with a 50 MHz thickness resonant frequency, were compared to those of a KLM model [R. Krimholtz, D.A. Leedom, G.L. Matthei, New equivalent circuit for elementary piezoelectric transducers, Electron. Lett. 6 (1970) 398–399] in the one-dimensional case. The acoustical properties were also found to be in good agreement with those obtained using the finite element (FE) method of ATILA^® software in two-dimensional configuration.     

Modeling of piezoelectric transducers with combined pseudospectral and finite-difference methods

A new hybrid finite-difference (FD) and pseudospectral (PS) method adapted to the modeling of piezoelectric transducers (PZTs) is presented. The time-dependent equations of propagation are solved using the PS method while the electric field induced in the piezoelectric material is determined through a FD representation. The purpose of this combination is to keep the advantages of both methods in one model: the adaptability of FD representation to model piezoelectric elements with various geometries and materials, and the low number of nodes per wavelength required by the PS method. This approach is implemented to obtain an accurate algorithm to simulate the propagation of acoustic waves over large distances, directly coupled to the calculation of the electric field created inside the piezoelectric material, which is difficult with classical algorithms. These operations are computed using variables located on spatially and temporally staggered grids, which attenuate Gibbs phenomenon and increase the algorithm's accuracy. The two-dimensional modeling of a PZT plate excited by a 50 MHz sinusoidal electrical signal is performed. The results are successfully compared to those obtained using the finite-element (FE) algorithm of ATILA software with configurations spatially and temporally adapted to the FE requirements. The cost efficiency of the FD-PS time-domain method is quantified and verified.     

Influence of acousto-optic interactions on the determination of the diffracted field by an array obtained from displacement measurements

This paper deals with the influence of acousto-optic interactions on the displacement measurements performed over transducer array and their effects on the predicted diffraction field. Changes on the temporal/spatial responses and the plane wave decomposition of the displacement are discussed. Modifications made on the directivity pattern are shown. A theoretical analysis of acousto-optic phenomenon, based on the plane wave decomposition of radiated field by the array is developed. Theoretical and experimental results are compared, showing first that waves with phase velocity near the one of the fluid are greatly amplified. Second, the interaction of laser beam with edge wave produced by the vertical size of elements induces a parasitic temporal pulse on the x-t diagram and so an interference pattern in the omega-k diagram. Corrections are proposed to eliminate errors induced by acousto-optic interactions and validated by comparing predicted diffraction field with measurements.     

Characterization of airborne transducers by optical tomography

This paper describes the application of an acousto-optic method to the measurement of airborne ultrasound. The method consists of a heterodyne interferometric probing of the pressure emitted by the transducer combined with a tomographic algorithm. The heterodyne interferometer measures the optical phase shift of the probe laser beam, proportional to the acoustic pressure integrated along the light path. A number of projections of the sound field, e.g. a set of ray integrals obtained along parallel paths, are made in moving the transducer to be tested. The main advantage of the method is its very high sensitivity in air (2 x 10(-4) Pa Hz-1/2), combined with a large bandwidth. Using the same principle as X-ray tomography the ultrasonic pressure in a plane perpendicular to the transducer axis can be reconstructed. Several ultrasonic fields emitted by wide-band home made electrostatic transducers, with operating frequencies between 200 and 700 kHz, have been measured. The sensitivities compared favorably with those of commercial airborne transducers.     

A multiscale model for array of capacitive micromachined ultrasonic transducers

A model is developed for studying the acoustic behavior of a cMUT array. This model is based on separate calculations of the terms describing the behavior of a single cMUT on one hand, and those corresponding to acoustic mutual coupling on the other hand. The terms are combined into an equivalent circuit with matrix terms which displays only one degree of freedom per cell. This approach allows the simulation of several dozen cMUTs considered individually with a very short computer time. A Finite Difference model is used for the simulation of an isolated cell radiating acoustic energy and the determination of its equivalent electromechanical circuit. It is shown for various mutual coupling situations that the coupling between cells can be correctly approximated using a very simple mutual impedance term. The model is compared with experimental results, using a set of different cMUT configurations. Experimental results were obtained with electrical impedancemetry and laser interferometry techniques performed in fluid immersion.     

Experimental and theoretical determination of 1-3 piezocomposite electroacoustic tensor

We report the development of two methods for determining the effective electroacoustic tensor of 1-3 piezocomposite material, one experimental and one theoretical based on homogenization techniques. The main aim was to compare and validate the results provided by these approaches. The slowness surfaces of bulk wave were computed in the large wavelength domain and were fitted to obtain the effective properties of the composite. Model predictions are discussed and compared with the Smith's model. The experimental method is an inversion technique comparing measurement of transmission coefficient through the piezocomposite plate with the simulated coefficient. The accuracy and stability of the minimization procedure is discussed. Experimental results obtained from two piezocomposite test plates are presented and compared with theory.