A simplified transfer matrix approach for the determination of the complex modulus of viscoelastic materials

Nowadays, several analytical and numerical approaches are available for analysing the performance of materials used in noise and vibration control applications. All these methodologies require knowledge of a set of input parameters which, in the case of viscoelastic materials, could exhibit strong dependence on frequency in the entire audible range. The aim of this paper is to present a simplified transfer matrix approach for the determination of the complex modulus for longitudinal waves of isotropic viscoelastic materials as a function of frequency. To that effect, the tested material is excited by an electromagnetic shaker and longitudinal waves are investigated. Using a frequency sweep as an excitation signal, the time domain response is measured downstream and upstream of the sample itself. A velocity transfer function is measured and, by using a transfer matrix model of the experimental setup, the complex wave number for longitudinal waves and, consequently, the complex modulus can be determined once the Poisson’s ratio is known in advance. The results are presented and discussed for different materials and compared with well-established quasi-static and dynamic techniques

Caractérisation mécanique en basses fréquences des matériaux acoustiques

Ce travail porte sur le développement de techniques de caractérisation mécanique aux basses fréquences des matériaux poreux, tels que les mousse polymères et les matériaux fibreux, couramment utilisés pour réduire les nuisances sonores. Dans une permière partie un banc de caractérisation quasistatique en traction compression permettant de mesurer le module d'Young et le coefficient de Poisson de ces matériaux sur la plage de fréquence 1-100 Hz est présenté. Une attention particulière est portée à la recherche du domaine linéaire de mesure, à la dépendence en fréquence, à l'anisotropie et aux effets dynamiques et de couplage. La deuxième partie est consacrée à la validation d'une technique pour étendre la bande de fréquence de mesure mieux adaptée à l'utilisation industrielle de ces matériaux aux hautes fréquences. Cette technique, basée sur le principe de superposition fréquence-température, est validée pour les mousses polyuréthane. De plus, on montre que la caractérisation d'un seul module d'élasticité sur une large plage de fréquence est suffisante pour décrire la dépendance en fréquence de tous les modules d'élasticité du matériau. La demière partie présente un nouveau système expérimental pour la mesure dynamique du module de rigidité en flexion des plaques poroélastiques (cette configuration est souvent utilisée). L'inversion repose sur une analyse modale basée sur la méthode de Prony et sur un modèle de plaque basé sur la théorie de Biot, incluant les interactions fluide-structure dans la plaque. Les résultats obtenus sur un matériau fibreux sont satisfaisants alors que les résultats obtenus sur une mousse polyuréthane montrent les limites du modèle développé.This work deals with new caracterisation techniques of the mechanical properties of porous materials, such as polymeric foams and fibrous materials, currently used in sound absorbing applications. First, a quasistatic traction-compression experimental technic used to measure Young's modulus and Poisson's ratio of such materials on the frequency range 1-100 Hz is described. A special attention is paid on linear domain, frequency dependence, anisotropy and dynamical and coupling effects. Next a most adapted to industrial context technic allowing a large frequency range carcterisation is presented. This technic, based on the frequency-temperature superposition principle, is validated on polyurethan foams. Moreover, it is shown that the knowledge of the frequency dependence of one modulus is enougth to predict the frequency dependance of all moduli. These materials being usually plate like, the final part presents a new experimental device to measure the bending modulus of poroelastic plates. The inversion is based on modal analysis with the Prony method and on a analytical model of bending behaviour of poroelastic plates. This model is based on the Biot model in order to take into account the fluid-strucure coupling effects. Results obtained on a fibroux material are satisfying while results obtained on a polymeric foam show clearly the limits of this new model.LE MANS-BU Sciences (721812109) / SudocSudocFranceF

Satisfaction Indicators Taking into Account the Measurement and Computation Uncertainties for the Comparison of Data in Electromagnetics: Motivations and Scheduled Tasks of the French National Working Group CDIIS

International audienceA national study of criteria able to provide a satisfaction indicator about the comparison of data from electromagnetic measurement and computation, taking into account their associated uncertainties, has been organized in the framework of a French Working Group of the GdR Ondes, called CDIIS (Com-paraison de Données entachées d'Incertitudes: Indicateurs de Satisfaction). This Working Group involves several industrial or academic research laboratories, including laboratories depending on governmental organisms. Four tasks have been defined: 1/ Identification of a set of satisfaction indicators. 2/ Identification of pertinent test cases in different application domains of elec-tromagnetics. 3/ Application of the above criteria on the test cases. 4/ Conclusions: which criterion is best adapted to a given electromagnetism problem. This paper deals with Task 1 and discusses the results of various indicators applied to a canonical RCS (Radar Cross Section) test case

Comparaison de critères permettant la comparaison de données entachées d'incertitude proposés par le Groupe de réflexion CDIIS du GdR Ondes

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