RESUMEN

A typical piezoelectric energy harvester is a bimorph cantilever with two layers of piezoelectric material on both sides of a flexible substrate. Piezoelectric layers of lead-based materials, typically lead zirconate titanate, have been mainly used due to their outstanding piezoelectric properties. However, due to lead toxicity and environmental problems, there is a need to replace them with environmentally benign materials. Here, our main efforts were focused on the preparation of hafnium-doped barium titanate (BaHfxTi1-xO3; BHT) sol-gel materials. The original process developed makes it possible to obtain a highly concentrated sol without strong organic complexing agents. Sol aging and concentration can be controlled to obtain a time-stable sol for a few months at room temperature, with desired viscosity and colloidal sizes. Densified bulk materials obtained from this optimized sol are compared with a solid-state synthesis, and both show good electromechanical properties: their thickness coupling factor kt values are around 53% and 47%, respectively, and their converse piezoelectric coefficient d33∗ values are around 420 and 330 pm/V, respectively. According to the electromechanical properties, the theoretical behavior in a bimorph configuration can be simulated to predict the resonance and anti-resonance frequencies and the corresponding output power values to help to design the final device. In the present case, the bimorph configuration based on BHT sol-gel material is designed to harvest ambient vibrations at low frequency (<200 Hz). It gives a maximum normalized volumetric power density of 0.03 µW/mm3/Hz/g2 at 154 Hz under an acceleration of 0.05 m/s2.

RESUMEN

Lead-based materials are widely used in piezoceramics due to their high electromechanical properties. However, due to environmental protection and sustainable development, the use of the toxic element lead (Pb) in electronic devices is strictly restricted, therefore requiring the rapid development of piezoelectric-based devices with lead-free ceramics. In this context, a lead-free doped barium titanate was studied with a dual objective. First, a new sol-gel method to synthesize Hf4+-doped BaHfxTi1-xO (BHT) with x = 0.05, 0.075, and 0.10 is presented. Such BHT sols were prepared at high concentrations of up to 1 M. Dilution in ethylene glycol allowed parameters (viscosity, colloid sizes, etc.) to be controlled, which ensured a time-stable sol for several months at room temperature. Second, densified bulk ceramics with attrited powders were obtained from these sols and showed very good electromechanical properties, with a thickness coupling factor of kt = 47% (BaHf0.05Ti0.95O3 sintered at 1500 °C/6 h). These results are a first step that will allow the processing of lead-free piezoelectric thick films using a sol-gel composite method for vibrational energy harvesting applications.

RESUMEN

This article deals with 2-D modeling of coupled vibrations of finite piezoelectric resonators. A general solution for all the physical quantities in the Cartesian and cylindrical coordinate systems is deduced from the governing equations by expansion in series summation of trigonometric functions of thickness coordinate and trigonometric or Bessel functions of the lateral one. The essential difference between this model and the earlier ones is that instead of expressing mainly in the thickness coordinate and integration through the thickness, the solutions are expressed in the form of double Fourier series augmented by single Fourier or Fourier-Bessel series, which contributes to better satisfy the mechanical and electrical boundary conditions. The dynamic stiffness matrix of the system is developed. Electrical impedances of a typical piezoelectric parallelepiped under stress-free and symmetrical loading conditions and its frequency spectrum for different width-to-thickness ratios are calculated using our model as well as by the finite element method. A comparison shows an excellent agreement. Finally, theoretical and measured electrical impedances of a piezoelectric parallelepiped and a piezoelectric disk are compared and discussed. The 2-D theoretical model proposed here is shown to be accurate and efficient for coupled vibration analysis of piezoelectric resonators and is applicable for any set of finite dimensions and crystal symmetry.

RESUMEN

The radial and thickness extensional vibration modes in piezoelectric cylinders are always inevitably coupled due to the finite dimension, Poisson's ratio, and piezoelectric effect. In this paper, an analytical model based on the superposition method is developed to obtain the coupled dynamic response of a piezoelectric cylinder under an applied voltage. The problem can be described mathematically by three partial differential equations with mixed boundary conditions in the cylindrical coordinates system. To solve this, the problem is decomposed first into two building block - vibrations in radial and thickness directions. In each building block, the expressions of displacements and electric potential are assumed and then the induced dynamic responses, such as in-plane stress and electric displacements, are calculated. Finally, the vibration responses of the two building blocks are superimposed to satisfy the mixed boundary conditions using Fourier and Fourier-Bessel series expansions. Electrical impedance of a typical piezoelectric disk and frequency spectrum of piezoelectric cylinders of different diameter-to-thickness ratios are calculated by the present analytical method as well as by finite element method. Comparison shows an excellent agreement. This analytical model can be applied to material characterization and the design and the optimization of the active elements of piezoelectric devices.

RESUMEN

Ultrasonic transducers performance can be seriously deteriorated by loss of adhesion between some constitutive elements such as the active element, the backing, or the matching layer. In the present work, the influence of bonding delaminations on the performance of a single-element ultrasonic transducer, which is composed of a piezoelectric disk, a backing, and a matching layer, is studied numerically and experimentally. Based on the positions between layers, two cases, i.e., delaminations between ceramic and backing or between ceramic and matching layer, are considered. Each case involves three different types of delaminations, which are marked as delamination type (DT)-I, II, and III. DT-I, a circular shape delamination, starts from the center and expands towards the peripheric zone; DT-II, an annular shape delamination, starts from the peripheric zone and expands towards the center; DT-III is a sector shape delamination with a given angle. The numerical simulations are performed by the finite element method and the influence of delaminations on the electromechanical admittance (EMA) of the transducer is investigated. 3D printed backings and matching layers are mounted on a PZT sample to assemble delaminated single-element transducers. An impedance analyzer is used for experimental measurements. Comparison between numerical and experimental results shows a reasonable agreement making changes in EMA an interesting indicator to inform about the occurrence and severity of delaminations in a single-element ultrasonic transducer.

RESUMEN

The transducer is an essential part of all ultrasonic systems used for applications such as medical diagnostics, therapy, nondestructive evaluation, and cleaning because its health condition is vital to their proper operation. Defects within the active element, backing or other constitutive elements, and loss of adhesion between layers can significantly weaken the performance of a transducer. The objective of this work is to determine procedures to monitor the behavior of a single-element probe during its lifetime and detect degradations before they significantly affect the performance of the system. To achieve this, electromechanical admittance (EMA)-based method is envisaged numerically and experimentally. A simplified single-element transducer consisting of a piezoceramic disk, a bonding layer, and a backing is studied and the influence of bonding delamination on EMA is investigated. This study considers three different types of delaminations, which are named, respectively, "center" (circular delamination from the center of the disk toward the peripheric zone), "peripheric" (annular delamination from the peripheric zone toward the center), and "wedge" (wedge-shaped delamination with a given angle). For each case, a numerical model based on the finite-element (FE) method is developed: a 2-D FE analysis is implemented for the first two types of delaminations, taking advantage of their axisymmetric structure, and "wedge" delamination is modeled in 3-D. Then, transducers with different shapes of 3-D printed backings are mounted and experiments are conducted using an impedance analyzer. Finally, experimental results are found to be in good agreement with numerical solutions and it shows that changes in EMA can particularly reveal the occurrence and extent of delamination in an ultrasound probe.

Asunto(s)

Transductores , Impedancia Eléctrica , Diseño de Equipo , Análisis de Elementos Finitos , Ultrasonografía

RESUMEN

In this paper, guided ultrasonic wave propagation is analyzed in an elastic plate with sinusoidal surface corrugations. The corrugated area acts as a finite-length grating which corresponds to a 1-D phononic crystal (PC). The multiple-scale perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. These equations are solved exactly for the two-point boundary-value problem of the PC. The study involves the coupling of the incident symmetric Lamb wave S(0) to the reflected antisymmetric Lamb wave A(0). The influences of the depth of corrugation and length of the PC are studied. Theoretical results are compared with experimental measurements.

RESUMEN

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. For this structure a mode-gap (mini stopband) occurs at low frequency: it involves the two fundamental Lamb modes A(0) and S(0). The numerical study is performed by using a finite element method (ATILA code). The experiments deal with a finite length grating and evanescent waves are characterized at the vicinity of the mini stopband.

RESUMEN

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. The goal of this work is to quantitatively establish the relation between the value of the attenuation of the propagating waves and the width of the forbidden bands appearing inside the Brillouin zone. This study is performed by using a finite element method (ATILA code).