Vibroacoustic inverse methods use the measured response of a vibrating structure to identify a structural parameter or a dynamic load. Two inverse methods are considered, the Force Analysis Technique (FAT) and the Virtual Fields Method (VFM). The Corrected Force Analysis Technique (CFAT) is a variant of FAT that corrects its singularity. This correction allows the method to be applied in the high-frequency domain, when the number of measurement points per flexural wavelength becomes small. In this study, the proposed novelty is the development of a Frequency-Adapted VFM (FA VFM) to the case of a Love-Kirchhoff plate. Thanks to this method, the VFM can now be applied to identify the equivalent bending stiffness and structural damping of a thin plate when the number of measurement points per wavelength is small. The method has previously been developed for an Euler-Bernoulli beam. An experimental identification of the complex bending stiffness of an locally damped aluminium plate using Laser Doppler Velocimetry (LDV) data and the developed method is performed. The experimental study shows for the first time that the FA VFM can be used to map the equivalent bending stiffness and structural damping as a function of position on a plate and identify these parameters as a function of frequency over a large frequency band. The results of the Frequency-Adapted VFM are compared with those of CFAT and the classical VFM approach. FA VFM results are more accurate than those of classical VFM and similar to those of CFAT.

The research presented in this paper aims to demonstrate how imperfect interfaces influence the behavior of a multilayered structure. To achieve this, a dynamic equivalent model for multilayered panels is used, enabling the characterization of these interfaces using experimental data. This model, known as the Layer Wise (LW) model, incorporates imperfections in the interfaces through sliding displacement. To effectively validate the model against experimental measurements, an equivalence with a thin beam is established. Then the experimental methodology used for characterization is outlined, including the setup, considered samples, and data processing techniques. Specifically, the Corrected Force Analysis Technique (CFAT) is used, which is a robust method based on the equations of motion for thin plates or beams. This method, for the first time, allows obtaining broadband frequency results, facilitating dynamic monitoring of interface states in multilayers. The concurrently developed model enables the quantification of an interface parameter through experimental measurements. Finally, a detailed analysis of the results obtained through this methodology is provided, emphasizing the significant influence of imperfect interfaces on the dynamics of multilayered structures.

We present the Sherbrooke-Lyon Research Training Program in Acoustics ("Projet Samuel de Champlain" 2022-2024, funded by the FRQNT: Fonds de recherche du Québec - Nature et technologies), which brings together teams from Université de Sherbrooke and from Master of Science in Acoustics of Lyon. This project aims to build a joint teaching program in acoustics through joint courses integrated into the graduate programs of the two institutions, research internships, and academic exchanges of students and researchers associated with the project. The joint courses are based on existing activities at the two institutions, whose content and teaching methods (mainly online) are adapted to the project. In the last two academic years, students from Sherbrooke followed the sound perception course of Lyon in co-modal modalities; and conversely, students from Lyon followed the smart acoustic lab module offered at UdeS in virtual mode. Three undergraduate students took also part in the program during their spring/summer internships (in the other partner lab, resp. CRASH and LVA), developing hybrid and virtual content (numerical laboratories). The presentation will focus mainly on how such innovative collaboration modalities can be applied in the context of education and research at university.

Inverse vibroacoustic methods can be used to identify the complex bending stiffness of a plate from its vibratory response. This work focuses on the Virtual Fields Method (VFM) and the Force Analysis Technique (FAT). The VFM uses functions called virtual fields to solve the Principle of Virtual Work, a weak form of equilibrium, and identifies complex bending stiffness. Here, the virtual fields are defined as piecewise functions over a surface smaller than the plate (virtual window). FAT uses a finite-difference scheme to discretize the fourth-order spatial derivatives of the displacement in the local equilibrium of the plate and thus estimates the bending stiffness. The application of a finite-difference scheme creates a bias in the identified stiffness, which increases with frequency. The Corrected Force Analysis Technique (CFAT) corrects this bias in the high-frequency domain. In this study, it is proposed to apply the CFAT principles to the VFM to adapt the method, using the virtual window size, so it can be applied it in the high-frequency domain. FAT, CFAT, the VFM and the Frequency-Adapted VFM will be presented. The method was tested on experimental data to identify the complex bending stiffness of an aluminium plate partially covered with a damping material.

This short communication evinces the ability of the CFAT methodology [Q. Leclère, JSV, 2015] to detect and characterize thickness-loss defects on homogeneous flat panels. A contactless measurement of the velocity field of an aluminium plate is performed by scanning laser vibrometry, from which the equivalent rigidity (apparent bending stiffness) is locally estimated within a wide frequency band in the ultrasonic domain. The method allows imaging thickness-reduction defects on the hidden face of an aluminium plate up to several hundreds of kilohertz. The first part details the experimental protocol, followed by a second enhancing the identification of the wavenumbers of symmetric S_0 and antisymmetric A_0 modes. The comparison with theoretical Lamb waves dispersion curves reveals the precision of the method. Finally, the methodology validates the possibility to precisely estimate the local material thickness and as a consequence the location, size and depth of a reference defect in the shape of a flat bottom hole (assuming homogeneous material properties of the plate).

In vibroacoustics, inverse methods use the vibratory response of a structure to identify either a load or a structural parameter. The Force Analysis Technique (FAT) and the Virtual Fields Method (VFM), are two inverse methods that have been used in the past to identify loads or structural parameters of flexural beams or plates. The Corrected Force Analysis Technique (CFAT) is another inverse method that corrects the singularity of FAT, making this approach more accurate at higher frequencies. In this study, this principle is applied to VFM, using a polynomial interpolation of the displacement field, to optimize the method. The accuracy of the optimized VFM is demonstrated using numerical simulations.

Honeycomb sandwich panels are widely used in the industry because of their outstanding stiffness to mass ratios. The dynamic response of such structures is known to be relatively complex especially in the mid-frequency domain where a strong orthotropy can be observed. Several equivalent models are available in the literature to understand and predict this behavior, all relying on an assumption that the geometry of the honeycomb core is periodic and perfectly known. The effect of imperfection inevitably introduced at the manufacturing stage are characterized in this work using X-ray measurements. A simple homogenization approach is proposed, allowing the prediction of the shearing properties of the core from statistics extracted from its geometry. These properties are used to predict the dynamic behavior of the structure using a multi-layer analytical model. Results are compared to Laser Doppler Vibrometer measurements, showing a very good agreement with the predictions based on X-ray pictures.

In vibroacoustics, inverse methods use the vibratory response of a structure to identify either a load or a structural parameter. The Force Analysis Technique (FAT) and the Virtual Fields Method (VFM), are two inverse methods that have been used in the past to identify loads or structural parameters of flexural beams or plates. The Corrected Force Analysis Technique (CFAT) is another inverse method that corrects the singularity of FAT, making this approach more accurate at higher frequencies. In this study, this principle is applied to the VFM, using polynomial interpolation of the displacement field, in order to adapt the method so that at each frequency, the accuracy of the method is improved. The accuracy of the Frequency-Adapted VFM is demonstrated using numerical simulations. A formal comparison between FAT, CFAT and the VFM is also proposed.

This works aims to build an equivalent model of multilayered structures with imperfect interfaces for vibro-acoustic modeling and characterization. To take into account imperfections, new interface conditions including constitutive equations, that describe the imperfections, are implemented. Once the displacement field with imperfect interfaces is obtained, the dispersion relation of the structure is derived from the equivalent model. The bending wavenumbers are then used to compute the equivalent flexural rigidity and the damping of the sandwich panel. In this paper, the methodology is applied to a sandwich panel with sliding interfaces. The equivalent parameters are computed and compared to the reference case, i.e. perfect interfaces model. The main impact of the imperfection on the results is a shift towards the low frequency of the equivalent parameter curves.

The aim of this paper is to propose a methodology for identifying the pressure field applied on a laminated composite plate from its measured vibration response. The general framework of this study is the Corrected Force Analysis Technique (CFAT), which was previously used on isotropic plates. This method estimates the spatial derivatives of the equation of motion with a finite difference scheme and corrects the bias error generated by this approximation. The paper presents an extension of this technique to deal with laminated panels. In a first instance, the finite difference scheme has been expanded to allow the identification of the 5 spatial derivatives that compose the equation of motion of such structures. The correction, considered in the wavenumber domain, has also been adapted and is now calculated numerically. In a second instance, the effect of measurement noise has been treated with the implementation of a regularisation technique based on the adaptation of the size of the scheme as function of the frequency. Numerical simulations and contact-less measurements have been conducted on different carbon fibers composite plates. Results are presented in terms of identified pressure fields and input force magnitude. (C) 2020 Elsevier Ltd. All rights reserved.

This paper deals with the dynamic characterisation of plate structures with elliptical orthotropic stiffness properties, using an equivalent thin plate theory using a wave fitting approach. The method consists in projecting the experimentally determined transverse displacement field of a plate on an analytical Green's function of an elliptical orthotropic plate based on Hankel's functions. The error between the projected and measured fields is then minimized, varying the characteristics of the function until an optimal fit is reached. The thus obtained characteristics are the two flexural rigidities defining the elliptical orthotropy of the plate, and the orthotropy angle. This fitting procedure is applied at each frequency, enabling the determination of frequency dependent dynamic material proper ties. The method is applied to a honeycomb sandwich panel to validate the proposed fit ting approach. The identified flexural rigidities are compared to the estimations obtained by means of an analytical model and the IWC (Inhomogeneous Wave Correlation) method assuming three different type of plate characteristics (anisotropic, orthotropic and elliptical orthotropic). For the elliptical orthotropic assumption, consistent results are observed between the methods and the model over a large frequency range (from 1 to 50 kHz). (C) 2020 Elsevier Ltd. All rights reserved.

Multilayered structures have shown their interest in today?s transportation and construction industries for their performances in term of high stiffness, lightweight or controlled damping that classical materials cannot offer. They are commonly used in automotive, aerospace or civil applications to lighten structures or reduce the vibration level and improve the sound insulation. In this context, several analytical models of such structures exist in literature to describes their dynamic behaviour. Car Condensed models are used to describe the dynamic behaviour of a multilayer structure by means of an equivalent homogeneous layer defined by intrinsic properties. Existing condensed models mainly describe the bending, membrane and shearing motions of the multilayer plate and neglect its dilatational motion. As a result, the transmission loss across the multilayer may be underestimated if the layers are soft and thick. In this paper, a condensed model of physically symmetric multilayer is developed. The antisymmetric and symmetric motions of the structure are described separately by means of two equivalent admittances. These admittances depend on three intrinsic properties: a dynamic bending stiffness and two dynamic mass densities. The condensed model is validated comparing transmission loss computations with the Transfer Matrix Method for multilayers with elastic or poroelastic cores. (c) 2021 Elsevier Ltd. All rights reserved.

The design of pianos is mainly based on empirical knowledge due to the lack of a simple tool that could predict sound changes induced by changes of the geometry and/or the mechanical properties of the soundboard. We present the framework of a program for the Computer-Aided Design of piano soundboards that is intended to bridge that gap by giving piano makers a tool to synthesize tones of virtual pianos. The sound synthesis is solely based on physical models of the instrument in playing situation. The calculation of the sound is split into several modules: computation of the modal basis of the stiffened soundboard, computation of the string dynamics, simulation of the soundboard dynamics excited by the string vibration, and calculation of the sound radiation. Reference tests of sound synthesis of real pianos as well as sound synthesis of modified pianos are used to assess our main objective, namely to reflect faithfully structural modifications in the produced sound, and thus to make this tool helpful for both piano makers and researchers of the musical acoustics community.

This paper presents the modelling and the dynamic characterisation of laminated composite plates and sandwich structures in terms of stiffness and damping. The developments used in this paper are based on the analytical multilayer model of Guyader and Lesueur (JSV, 1978). The model considers linear shear, membrane and bending effects in each layer. The characteristics of the structure are determined by means of an equivalent thin plate methodology. The first main novelty of this paper consists in adapting this methodology for laminated plates (orthotropic multilayers with arbitrary orthotropic angle per layer). An experimental validation of this adaptation is presented for a laminated composite plate. Concerning the modelling of the structural loss factor, a space domain definition based on the spatial attenuation of a plane wave is compared to an energetic method and an equivalent definition based on the thin plate theory. The results show that the equivalent definition overestimates the loss factor in high frequencies since the thin plate theory only considers the flexural behaviour of the structure. On the contrary, the space domain definition (which give similar results as compared to the energetic one for lightly damped structures) considers the frequency dependent variation of the dynamic behaviour of the structure by means of the ratio between the group and phase velocities. The latter approach is considered to be more correct. The second main novelty of this article is on the experimental validation of this space domain definition. The structural loss factors of two sandwich structures are identified from measurements using modal, energetic and spatial methods. The results using the space domain definition are in very good agreement with the analytical predictions and the estimations of the modal and energetic methods for both plates for a large frequency band (up to 20 kHz), demonstrating the validity of the approach developed in this paper. (C) 2020 Elsevier Ltd. All rights reserved.

This paper deals with the structural damping of mutilayered plates. Three definitions of loss factor are studied. The first one uses an equivalent methodology which assumes that the structure behaves as a Love-Kirchhoff's thin plate. The second approach links the spatial decay rate to the spatial decay rate by means of the group velocity of the wave to account for the dynamic behavior of the structure (shearing effect of the layers). The third approach relies on an energetic method based on the Modal Strain Energy (MSE) method. The loss factors according to these definitions are compared by means of an analytical model of multilayered plates for a typical sandwich structure. Experimental measurements are conducted on constrained-layer damping sandwich plates to validate the definitions. The loss factor is identified using three different protocols based on modal analysis (ESPRIT method), time decay rate estimation and displacement field analysis (CFAT method) and compared to the predictions of the analytical model.