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Formulas For Natural Frequency And Mode Shape

In the last 25 years, piezoelectric ceramic-polymer composites have been conceptualized, prototyped, fabricated, and implemented in an array of applications encompassing medical imaging and military missions, among others. A detailed snapshot of the materials used, and a detailed account of the major innovative methods developed in making various piezoelectric ceramic-polymer composites are presented. The salient aspects of processing of such composites are summarized, and structure-processing-property relations are described using connectivity as the unifying central concept. Computer-aided design (CAD)-based fabrication methods, which result in composites whose structural complexity surpass that of composites obtained with traditional methods, are described to introduce the reader to novel concepts in processing of piezocomposites. A brief survey of some recent advances made in modeling of (0-3), (1-3), and (2-2) composites also is provided.

Piezoelectric composites for sensor and actuator applications

This paper discusses the development of a 64-element 35-MHz composite ultrasonic array. This array was designed primarily for ocular imaging applications, and features 2-2 composite elements mechanically diced out of a fine-grain high-density Navy Type VI ceramic. Array elements were spaced at a 50-micron pitch, interconnected via a custom flexible circuit and matched to the 50-ohm system electronics via a 75-ohm transmission line coaxial cable. Elevation focusing was achieved using a cylindrically shaped epoxy lens. One functional 64-element array was fabricated and tested. Bandwidths averaging 55%, 23-dB insertion loss, and crosstalk less than -24 dB were measured. An image of a tungsten wire target phantom was acquired using a synthetic aperture reconstruction algorithm. The results from this imaging test demonstrate resolution exceeding 50 /spl mu/m axially and 100 /spl mu/m laterally.

Development of a 35-MHz piezo-composite ultrasound array for medical imaging

Ultrasound imaging at frequencies above 20 MHz is capable of achieving improved resolution in clinical applications requiring limited penetration depth. High frequency arrays that allow real-time imaging are desired for these applications but are not yet currently available. In this work, a method for fabricating fine-scale 2-2 composites suitable for 30-MHz linear array transducers was successfully demonstrated. High thickness coupling, low mechanical loss, and moderate electrical loss were achieved. This piezo-composite was incorporated into a 30-MHz array that included acoustic matching, an elevation focusing lens, electrical matching, and an air-filled kerf between elements. Bandwidths near 60%, 15-dB insertion loss, and crosstalk less than -30 dB were measured. Images of both a phantom and an ex vivo human eye were acquired using a synthetic aperture reconstruction method, resulting in measured lateral and axial resolutions of approximately 100 /spl mu/m.

A 30-MHz piezo-composite ultrasound array for medical imaging applications

Review of air-coupled ultrasonic materials characterization.

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

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.

A multiscale model for array of capacitive micromachined ultrasonic transducers

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...

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

A wide range of ultrasound methods has been proposed to assess the mechanical strength of bone. The axial transmission technique, which consists of measuring guided elastic modes through the cortical shell of long bones such as the radius or tibia, has recently emerged as one of the most promising approaches of all bone exploration methods. Determination of dispersion curves of guided waves is therefore of prime interest because they provide a large set of input data required to perform inverse process, and hence to evaluate bone properties (elastic and geometric). The cortical thickness of long bones ranges from approximately 1 to 7 mm, resulting in wide inter-individual variability in the guided wave response. This variability can be overcome by using a single probe able to operate with a tunable central frequency, typically within the 100 kHz to 2 MHz frequency range. However, there are certain limitations in the design of low-frequency arrays using traditional PZT technology; these limitations have triggered active research to find alternative solutions. Capacitive micromachined ultrasonic transducers (cMUTs) have the potential to overcome these limitations and to improve axial transmission measurement significantly. The objective of this study was to design and construct a new cMUT-based axial transmission probe and to validate the approach. We report all the steps followed to construct such a prototype, from the description of the fabrication of the cMUT (based on a surface micromachining process) through probe packaging. The fabricated device was carefully characterized using both electrical and optical measurements to check the homogeneity of the device, first from cMUT to cMUT and then from element to element. Finally, axial transmission measurements carried out with the prototype cMUT probe are shown and compared with results obtained with a PZT-based array.

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A capacitive micromachined ultrasonic transducer probe for assessment of cortical bone

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...

Dominique Certon

Papers

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

A multiscale model for array of capacitive micromachined ultrasonic transducers

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

A capacitive micromachined ultrasonic transducer probe for assessment of cortical bone

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