Dominique Certon

A matrix method for modeling electroelastic moduli of 0-3 piezo-composites

A model is proposed to predict the electroelastic moduli of 0-3 connectivity piezo-composites from which parameters such as longitudinal wave velocity and thickness mode coupling factor can be deduced. The composite, a polymer loaded with ceramic particles, is represented by a unit cell, and a matrix manipulation is shown to be a practical way to perform a generalization of the series and parallel analysis used for 2-2 connectivity composites. The anisotropy of the ceramic phase is taken into account, and its effect on the properties of the composite is shown. The model is then used to optimize composite performance and to choose the two constituents through comparison of results obtained using several commercial polymers and ceramics.

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.

Investigation of cross-coupling in 1-3 piezocomposite arrays

Plate waves inside the piezoelectric layer are much involved in the element cross-coupling in transducer arrays for medical imaging. In this work, such waves are analyzed in 1-3 piezocomposite materials on the basis of conventional guided modes formalism in which the piezocomposite is considered as a homogeneous medium. Cross-coupling measurements have been made on two different transducer arrays using a network analyzer and a laser interferometric probe. It is shown how the analysis in terms of symmetrical Lamb waves gives an interesting qualitative interpretation, explaining most of the cross-coupling amplitude variations with frequency. Results show that the 0th and 3rd symmetrical Lamb waves are mainly involved in coupling inside composite plates. The S/sub 0/ mode is responsible for the inter-element coupling, whereas the S/sub 3/ mode widens the effective width of the excited element.

Lateral resonances in 1–3 piezoelectric periodic composite: Modeling and experimental results

The objective of this work is to provide an accurate model of the lateral resonance modes in 1–3 piezoelectric composite materials. These materials are widely used in ultrasonic transducers and the lowest lateral mode frequency gives the upper limit for the usable transducer bandwidth. Considering the propagation of purely transverse waves in a 2-D periodic medium of infinite thickness, two different approaches for obtaining the solutions are presented and compared. The first approach is based on the use of the Bloch waves theory. The second is a straightforward method (a so-called membrane method) which consists in numerically solving the propagation equation in the two-phase medium while taking into account the periodic boundary conditions. Methods based on both models are described that allow the calculation of the dispersion curves and the stop band limits, as well as the frequencies and the displacement fields of the lateral modes. A test case is used to compare and discuss the theoretical prediction...

Experimental determination of the surface acoustic wave properties of new fine grain piezoelectric ceramics

The surface acoustic wave (SAW) properties, i.e., free surface wave velocity, surface coupling coefficient, and static surface permittivity, of a lead titanate composition modified with an additive of samarium and processed by hydrothermal synthesis are determined. The effective permittivity of the piezoelectric ceramic was calculated, and the SAW properties were extracted from the analysis of the curve. In particular, the relations between the square coupling coefficient, the effective permittivity, and the usual definition k2s=2ΔV/V are discussed. In parallel, experimental measurements of the SAW properties were carried out by developing a curve‐fitting algorithm on the real and imaginary parts of a unapodized single electrode SAW transducer. A free surface wave velocity of 2595 m/s, a coupling coefficient of 1.8%, and a static permittivity of 196 are found which were predicted by the analysis of the effective permittivity curves. The SAW properties of a Y+128° cut lithium niobate single crystal are als...

Theoretical and experimental investigations of lateral modes in 1-3 piezocomposites

Materials with a periodic microstructure show resonances caused by the elastic wave Bragg diffraction. This paper presents a simple approach to describe these resonances (called lateral resonances) in 1-3 piezoelectric composite materials which have a 2-D periodicity. Our model is based on the analysis of the propagation of transverse waves in a 2-D periodic medium of infinite thickness and takes into account the periodic and interfacial boundary conditions. This model predicts the displacement field vectors and frequencies of lateral resonances from which the phase velocity of lateral waves is determined. The theoretical and experimental variations of this velocity versus the ceramic rod width to pitch ratio are compared. It is shown that the first lateral mode frequency is maximum when the ceramic volume fraction is around 0.65. Theoretical predictions of the mechanical displacement at the composite surface are compared with measurements obtained by an interferometric laser technique. A good agreement is observed, showing that lateral waves are mainly vertically polarized.

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 algorithms 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.

Tissue harmonic imaging with CMUTs

In this work, we report on the characterization of a CMUT probe (Capacitive Micromachined Ultrasound Transducer) for Tissue Harmonic Imaging (THI). The intrinsic nonlinear behavior of the CMUT probe was first investigated. Matched electrical waveforms were transmitted to limit the impact of the transmit response distortion. With the implemented method, we demonstrated higher performances through in-vitro harmonic imaging.

Fast time-domain modeling of fluid-coupled cMUT cells: from the single cell to the 1-D linear array element

We report a fast time-domain model of fluid-coupled cMUTs developed to predict the transient response-i.e., the impulse pressure response-of an element of a linear 1-D array. Mechanical equations of the cMUT diaphragm are solved with 2-D finite-difference schemes. The time-domain solving method is a fourth-order Runge-Kutta algorithm. The model takes into account the electrostatic nonlinearity and the contact with the bottom electrode when the membrane is collapsed. Mutual acoustic coupling between cells is introduced through the numerical implementation of analytical solutions of the impulse diffraction theory established in the case of acoustic sources with rectangular geometry. Processing times are very short: they vary from a few minutes for a single cell to a maximum of 30 min for one element of an array. After a description of the model, the impact of the nonlinearity and the pull-in/pull-out phenomena on the dynamic behavior of the cMUT diaphragm is discussed. Experimental results of mechanical displacements obtained by interferometric measurements and the acoustic pressure field are compared with simulations. Different excitation signals-high-frequency bandwidth pulses and toneburst excitations of varying central frequency-were chosen to compare theory with experimental results.

Experimental investigation of cross-coupling and its influence on the elementary radiation pattern in 1D ultrasound arrays

Cross-coupling mechanisms in ultrasound arrays have deep influences on their performances. Here, to investigate them, the surface displacement of a 1D linear array is measured in water with a laser interferometer. Displacement data are then analyzed in both Time-Space and in Time frequency-Spatial frequency domains. Radiation pattern is then simulated from this data and compared to the radiation pattern of a plane piston and to hydrophone measurements. Cross-coupling influence on the 1D array element behavior is finally compared and discussed. Laser interferometry is shown to be a useful tool for ultrasound array optimization as it allows the identification of vibration modes, the determination of the elementary effective aperture and the radiation pattern of elements.