Marc Lethiecq

The acoustical modelling of multilayered systems is crucial for researchers and engineers aiming to evaluate and control the behaviour of complex media and to determine their internal properties. In this work, we first develop a forward model describing the propagation of acoustic waves through various types of materials, including fluids, solids, and poroelastic media. The model relies on the classical theoretical frameworks of Thomson and Haskell for non-porous layers, while Biot’s theory is employed to describe wave propagation in poroelastic materials. The propagation is mathematically treated using the transfer matrix method, which links the acoustic displacement and stress at the extremities of each layer. Appropriate boundary conditions are applied at each interface to assemble all local matrices into a single global matrix representing the entire multilayer system. This forward model allows the calculation of theoretical transmission coefficients, which are then compared to experimental measurements to validate the approach proposed. Secondly, this modelling framework is used as the basis for solving inverse problems, where the goal is to retrieve unknown internal parameters, such as mechanical or acoustic properties, by minimizing the discrepancy between simulated and experimental transmission spectra. This inverse problem approach is essential in non-destructive evaluation applications, where direct measurements are often unfeasible.

Multilayer piezoelectric stacks, which are multiple layers of piezoelectric materials placed on top of each other, are widely used to achieve precise linear movement and high-force generation. In this paper, a dynamic stiffness (DS) method for the dynamic vibration analysis of multilayer piezoelectric stacks is presented. First, the general solutions for all physical quantities of the three vibration contributions (i.e., pure vibration, symmetrically coupled vibration, and anti-symmetrically coupled vibration) are derived from the governing equations of motion. Then, the DS matrices of each layer of the piezoelectric stack are obtained, and they are assembled to form a global DS matrix. The electrical impedances and the mode shapes of a piezoelectric stack consisting of two piezoelectric disks connected in series and in parallel are calculated using our method as well as by the finite element method. The comparison shows good agreement. Finally, the effect of the number of layers on the dynamic responses of piezoelectric stacks is investigated. The DS method developed here provides an efficient and accurate analytical tool for the parametric and optimization analysis of the coupled vibrations of multilayer piezoelectric structures.

Improving the performance of high-temperature ultrasonic transducers is a goal of major importance in many industrial applications. To this aim, we propose to use porous metals that support high temperatures as backings. Thus, the acoustic properties of stainless steel and porous stainless steel with porosity of 25% and 35% are determined at ambient temperature and up to 400 °C. Over the temperature range, the longitudinal wave velocity variation is comprised between 5% and 6% in the porous metals. We find that temperature does not significantly affect the attenuation in the material. The pulse-echo response and frequency response of a LiNbO3-based transducer with a porous backing are simulated using a one dimensional electroacoustic model. These simulations, compared to those of a reference transducer, show that the axial resolution with such a design allows these transducers to be used for imaging and/or Non-Destructive Testing and evaluation at high temperature.

Paintings are intricate structures made up of multiple layers of materials that possess different properties and thicknesses. Due to their fragility, they can be damaged by exposure to various environmental factors such very large amplitude vibrations, as well as temperature and humidity variations. Restorers use various techniques such as raking light, x-rays, infrared, and UV to gather information about the condition of the artwork. Unlike these methods, ultrasonic techniques use elastic waves and can thus provide information about the mechanical properties of the materials and their interfaces. The goal of this work is twofold. First, it consists in numerically analyzing the sensitivity of elastic parameters of painting layers through their influence on the acoustic transmission coefficient and dispersion curves. Then, an experimental device is set up to confirm some of these results by the determination of the values of the elastic parameters of the constituent layers of paintings. To this aim, we have developed an original association of numerical and experimental methods for characterization and determination of the layer elastic parameters of some materials used in paintings. A matrix stiffness model associated to a genetic algorithm are used for the numerical study and optimization process between the theoretical transmission coefficient and the experimental one. Then, focused Air-Coupled Transducers (ACTs) in conjunction with a rotary motor are used to perform measurements of transmitted signal amplitude on several components used in paintings under various angles of incidence. Our results concerning the determination of elastic parameters values on various materials including plexiglass (PMMA), acrylic paint, varnish, gesso and wood, taken as single plates, and bi-layered structures, are strongly supported by theoretical results obtained using the matrix stiffness model.

This paper presents the possibility of enhancement of the generation and detection of poorly energetic acoustic-guided waves in multilayered structures using a new design for a V(z) transducer. By defining a modified V(z) transducer composed of segmented piezoelectric elements, the acoustical energy can be directed towards specific angles in such a way as to generate guided waves that are poorly energetic. By comparing the results using this new design to those obtained with a classical V(z) transducer, it is shown that the generation and detection of such waves is greatly improved, especially for poorly energetic waves that belong to a buried layer in a multilayered structure. This is especially seen on the components of the spectra of V(z). The modeling of the modified V(z) signature for a multi-element focused transducer is widely detailed first. Then, in order to illustrate the advantages of our proposed method, a three-layer structure (aluminum/epoxy/steel) is discussed. The interest of this method for the characterization of elastic properties of “buried” layers through specific guided waves that are detected with great difficulty—or even not at all—with a classical V(z) transducer is demonstrated, especially for the A₀ and S₀ modes corresponding to the steel layer inside the three-layer structure. In this study, we also develop a specific tracking method for particular guided waves possessing large phase velocity variations over the considered frequency range, as is the case for the S₀ mode of the steel sub-layer.

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.

In order to assess the health of cultural heritage paintings, for example prior to their restoration, visual inspections as well as techniques such as X-ray imaging are commonly used. Non-contact acoustic methods could become another exploration modality thanks to their non-destructive character and the fact that they are expected to be more sensitive to certain defects, such as a delamination, than other techniques. A setup has been designed for such applications, based on airborne ultrasonic transducers operating in the several hundred kHz to over 1 MHz range, specific transmit/receive electronics and automated scanning stages allowing 2D through-transmission scans to be performed on areas up to 80 × 80 square centimeters. Measurements on well-known thin plates made of plastic, wood and gesso on wood were first performed to evaluate the possibilities of the technique, then simple paintings on canvas were tested and finally a real ancient painting was scanned. A method where the transmission amplitude is plotted versus the angle between the propagation axis and the normal to the painting surface is developed for local characterization of the elastic constants of the sample under test, thanks to comparison with simulated Lamb wave dispersion curves using a fitting procedure. These promising results open the way towards comparison between acoustic, radiological and other imaging results on paintings with severe defects that require restoration.