Homogenization of periodic 1-3 piezocomposite using wave propagation: Toward an experimental method.

1-3 piezocomposites are first choice materials for integration in ultrasonic transducers due to their high electromechanical performance, particularly, in their thickness mode. The determination of a complete set of effective electroelastic parameters through a homogenization scheme is of primary importance for their consideration as homogeneous. This allows for the simplification of the transducer design using numerical methods.

Modeling the Electroelastic Moduli of Porous Textured Piezoceramics.

A new model for piezoelectric textured ceramics was developed that considers the presence of porosity, which can appear during heat treatment (ceramic sintering). In the long wavelength approximation, a matrix method, which has already been applied to piezoelectric composites, was extended to textured ceramics for three phases [porosity (air), piezoelectric single-crystal (related to the texturation degree), and ceramic] to calculate the effective electroelastic modulus. This method was first compared and validated with finite-element calculations.

Electrical Evidence of the Tunable Electrical Bragg Bandgaps in Piezoelectric Plates.

A piezoelectric plate, poled along its thickness and supporting on its top and bottom surfaces a periodic grating of electrodes, is considered. An analytical model allowing band structure calculation is derived for the first symmetrical mode propagating along the length of the plate. Analytical results show that an electrical Bragg (EB) bandgap can be observed for this mode, depending on the electrical boundary conditions applied on the electrodes.

Super-Cell Piezoelectric Composite With 1-3 Connectivity.

The standard fabrication method for 1-3 piezocomposites for ultrasound transducers is the "dice and fill" method (DFM) in which lateral periodicity is introduced. This contributes to the appearance of spurious modes that can drastically affect the performance of the device if they appear near its thickness mode frequency, thus limiting the effective frequency range. A new 1-3 piezocomposite fabricated with a super-cell structure [1-3 super cell (13SC)] was designed in order to overcome these limitations.

Tunable phononic crystals based on piezoelectric composites with 1-3 connectivity.

Phononic crystals made of piezoelectric composites with 1-3 connectivity are studied theoretically and experimentally. It is shown that they present Bragg band gaps that depend on the periodic electrical boundary conditions. These structures have improved properties compared to phononic crystals composed of bulk piezoelectric elements, especially the existence of larger band gaps and the fact that they do not require severe constraints on their aspect ratios.

Control of elastic wave propagation in one-dimensional piezomagnetic phononic crystals.

Two ways of controlling the acoustic waves propagation by external inductance or capacitance in a one-dimensional (1-D) piezomagnetic phononic crystal are investigated. The structure is made of identical bars, constituted of a piezomagnetic material, surrounded by a coil and connected to an external impedance. A model of propagation of longitudinal elastic waves through the periodic structure is developed and the dispersion equation is obtained.

Theoretical and experimental analyses of tunable Fabry-Perot resonators using piezoelectric phononic crystals.

Theoretical and experimental analyses of piezoelectric stacks submitted to periodical electrical boundary conditions via electrodes are conducted. The presented structures exhibit Bragg band gaps that can be switched on or off by setting electrodes in short or open circuit. The band gap frequency width is determined by the electromechanical coupling coefficient.

Focusing capability of a phononic crystal based on a hollow metallic structure.

The dispersion curves of a phononic crystal (PC) based on a hollow metallic structure are presented. They exhibit a negative refraction dispersion branch and perfect refractive index matching with the surrounding water, leading to focusing capability. Numerical and experimental results are reported for a flat PC lens.

Analysis of signals propagating in a phononic crystal PZT layer deposited on a silicon substrate.

The design of a stop-band filter constituted by a periodically patterned lead zirconate titanate (PZT) layer, polarized along its thickness, deposited on a silicon substrate and sandwiched between interdigitated electrodes for emission/reception of guided elastic waves, is investigated. The filter characteristics are theoretically evaluated by using finite element simulations: dispersion curves of a patterned PZT layer with a specific pattern geometry deposited on a silicon substrate present an absolute stop band. The whole structure is modeled with realistic conditions, including appropriate interdigitated electrodes to propagate a guided mode in the piezoelectric layer.

Experimental and numerical study of evanescent waves in the mini stopband of a 1D phononic crystal.

This paper deals with the analysis of the guided evanescent waves in stopbands of a 1D phononic crystal (PC). A new numerical implementation is shown in order to get the complex values of the wavenumbers in a frequency range where a gap occurs. The considered phononic system is an aluminum plate with a one-dimensional sinusoidal grating.

Analysis of elastic waves transmitted through a 2-D phononic crystal exhibiting negative refraction.

A two-dimensional phononic crystal (PC) made of a square lattice of air holes in an aluminum matrix is studied. The band structure calculated in the irreducible Brillouin zone of the PC exhibits a branch with a negative slope that allows negative refraction. This phenomenon has been numerically verified using a prism-shaped PC for plane waves entering the PC with two different incidences.

Attenuation of Lamb waves in the vicinity of a forbidden band in a phononic crystal.

When a Lamb wave propagates on a plate engraved by a periodic grating, it may exhibit attenuation. This attenuation is related to a coupling of this incident mode with other propagating modes. As the propagation takes place in a periodic medium, the dispersion curves of the modes are of interest because they exhibit passbands and stopbands related to the geometry of the waveguide.

Experimental validation of band gaps and localization in a one-dimensional diatomic phononic crystal.

The propagation of compressional ultrasonic pulses through a finite one-dimensional chain of various unit cells is investigated experimentally. The chain, initially compressed by an axially applied constant force, is excited by a periodic force, which acts in line with axis of bead chain. The experimental measurements giving the eigenfrequencies of the specimen are based on a Fourier analysis of the transmitted acoustic pulse.

Miniature multimode monolithic flextensional transducers.

Traditional flextensional transducers classified in seven groups based on their designs have been used extensively in 1-100 kHz range for mine hunting, fish finding, oil explorations, and biomedical applications. In this study, a new family of small, low cost underwater, and biomedical transducers has been developed. After the fabrication of transducers, finite-elements analysis (FEA) was used extensively in order to optimize these miniature versions of high-power, low-frequency flextensional transducer designs to achieve broad bandwidth for both transmitting and receiving, engineered vibration modes, and optimized acoustic directivity patterns.

Numerical homogenization techniques applied to piezoelectric composites.

With the recent availability of piezoelectric fibers, the design and the analysis of piezoelectric composites needs new modeling tools. Therefore, a numerical homogenization technique has been developed, based on the ATILA finite element code, that combines two techniques: one relying upon the representative volume element (RVE) the other relying upon the wave propagation (WP). The combination of the two methods allows the whole tensor of the homogenized properties of the piezoelectric composite to be found.

On the existence of subresonance generated in a one-dimensional chain of identical spheres.

In this paper, the propagation of short compressional pulses through a one-dimensional chain of identical spherical beads is analyzed. First, a single sphere is studied. Then, an infinite chain of identical spheres is considered.