Damping analysis of a free aluminum plate

International audienceAn analysis of the energy dissipation sources acting in a vibrating aluminum plate is pre10 sented in this paper. In a first step, the contact-free modal analysis of a suspended plate 11 is conducted using a laser vibrometer and an acoustic excitation to obtain reference data. 12 The thin nylon suspension set-up guarantees a low boundary damping, which is assumed 13 to be negligible. In a second step, a number of damping sources are modeled. Acoustic 14 damping due to the noise radiation of the non-baffled plate is computed using the boundary 15 integral method and a light fluid approximation to express the vibroacoustic coupling in 16 analytical terms. The damping due to the sheared air flow along the free plate borders is 17 determined on the basis of a simple two-dimensional boundary layer model. Thermoelastic 18 damping is assessed using a Fourier series expression for the temperature field along with a 19 perturbation technique to take thermoelastic coupling into account. Since no robust model 20 is available so far to quantify viscoelastic material damping in aluminum, it is determined 21 in a last step by subtracting measured values of damping to the one that have previously 22 been computed. Aluminum viscoelastic damping turns out to be very small and almost 23 independent of frequency

Optimisation vibroacoustique de structures amorties par des traitements en élastomère

This work is devoted to the modelling of damped structures and to the optimization of elastomer treatments for noise reduction purposes. The damping of a suspended aluminium plate partially covered by a constrained elastomer treatment has been identified in a first step through a contact-free modal analysis. A precise and systematic quantification of the main dissipation sources has then been carried out; while the thermoelastic dissipation in the aluminium, the dissipation due to air viscosity and to the acoustic radiation have been modelled, the viscoelastic dissipations within the aluminium and the elastomer have been identified. The thermoelastic computation, based on a perturbation approach to solve the coupled problem, highlights the limits of Zener's model, considered as a reference. The modelling of the elastomer relies on an identification experiment of its complex frequency-dependent stiffness modulus. A resolution platform based on the computation of the resonance modes with a finite element program, a complex eigenvalue solver as well as iterative and perturbation routines has been developped in order to account for any specific type of damping. The final algorithm can compute the instationary time/frequency response of systems with a general unproportional linear damping very rapidly and precisely. In a last part, parametric optimization studies give a fine understanding of the influence of elastomer damping treatments as well as a practical know-how in the area of noise reduction.Le travail présenté dans ce mémoire est une contribution à la modélisation vibratoire de structures amorties et à l'optimisation de traitements en élastomère pour la réduction de bruit. Une méthode d'analyse modale sans contact a permis d'identifier dans un premier temps l'amortissement structurel total d'une plaque en aluminium suspendue, traitée par des patches en élastomère contraint. Une quantification précise des principales sources de dissipation a ensuite été effectuée. La dissipation thermoélastique de l'aluminium, visqueuse de l'air et la dissipation par rayonnement acoustique ont été modélisées; les dissipations viscoélastiques de l'aluminium et de l'élastomère, identifiées. Le calcul thermoélastique repose sur la prise en compte du couplage par perturbation et apporte quelques éclairages sur le modèle de référence de Zéner. La modélisation de l'élastomère s'appuie sur une expérience d'identification du module de rigidité complexe en fonction de la fréquence. Une plate-forme de résolution, basée sur le calcul des modes de résonance à l'aide de la méthode des éléments finis, d'un solveur aux valeurs propres complexe et de routines itératives et de perturbation, permet le calcul précis et rapide de la réponse temporelle ou fréquentielle instationnaire de systèmes à amortissement linéaire, non-proportionnel et dépendant de la fréquence. Dans une dernière partie, des études d'optimisation paramétrique conduites sur des traitements en élastomère débouchent sur un savoir-faire pratique en matière de réduction de bruit

Time and frequency response of structures with frequency dependent, non-proportional linear damping

International audienceA method to compute the non-stationary time and frequency response of structures with a frequency-dependent non-proportional linear damping, called the resonance modes method, is presented in this paper. It consists of two main steps. The first step aims at spotting the structure resonance modes, which are the solutions of the matrix non-linear eigenvalue problem obtained using the finite element method in the complex plane. This step requires a complex eigensolver and an iterative scheme, a perturbation technique or a combination of both. The second step uses the computed resonance modes and an analytical expression of the inverse Laplace transform to deduce the time or frequency response of structures to general excitations. The response of an aluminum plate damped with an elastomer treatment to a point-force excitation, computed with the classical modal approach, the direct solution and the presented method shows its precision and efficiency. An acoustic power computation finally validates the implementation of a fast variant, based on the perturbation technique, for vibroacoustic applications

High frequency FRF bound prediction for uncertain symmetrically-laminated composite plates

No description supplie

Optimisation vibroacoustique de structures amorties par des traitements en élastomère

Le travail présenté dans ce mémoire est une contribution à la modélisation vibratoire de structures amorties et à l'optimisation de traitements en élastomère pour la réduction de bruit. Une méthode d'analyse modale sans contact a permis d'identifier dans un premier temps l'amortissement structurel total d'une plaque en aluminium suspendue, traitée par des patches en élastomère contraint. Une quantification précise des principales sources de dissipation a ensuite été effectuée. La dissipation thermoélastique de l'aluminium, visqueuse de l'air et la dissipation par rayonnement acoustique ont été modélisées ; les dissipations viscoélastiques de l'aluminium et de l'élastomère, identifiées. Le calcul thermoélastique repose sur la prise en compte du couplage par perturbation et apporte quelques éclairages sur le modèle de référence de Zéner. La modélisation de l'élastomère s'appuie sur une expérience d'identification du module de rigidité complexe en fonction de la fréquence. Une plate-forme de résolution, basée sur le calcul des modes de résonance à l'aide de la méthode des éléments finis, d'un solveur aux valeurs propres complexe et de routines itératives et de perturbation, permet le calcul précis et rapide de la réponse temporelle ou fréquentielle instationnaire de systèmes à amortissement linéaire, non-proportionnel et dépendant de la fréquence. Dans une dernière partie, des études d'optimisation paramétrique conduites sur des traitements en élastomère débouchent sur un savoir-faire pratique en matière de réduction de bruitThis work is devoted to the modelling of damped structures and to the optimization of elastomer treatments for noise reduction purposes. The damping od a suspended aluminium plate partially covered by a constrained elastomer treatment has been identified in a first step through a contact-free modal analysis. A precise and systematic quantification of the main dissipation sources has then been carried out ; while the thermoelastic dissipation in the aluminium, the dissipation due to air viscosity and to the acoustic radiation have been modelled, the viscoelastic dissipations within the aluminium and the elastomer have been identified. The thermoelastic computation, based on a perturbation approach to solve the coupled problem, highlights the limits of Zener's model, considered as a reference. The modelling of the elastomer relies on an identification experiment of its complex frequency-dependent stiffness modulus. A resolution platform based on the computation of the resonance modes with a finite element program, a complex eigenvalue solver as well as iterative and perturbation routines has been developped in order to account for any specific type of damping. The final algorithm can compute the instationary time/frequency response of systems with a general unproportional linear damping very rapidly and precisely. In a last part, parametric optimization studies give a fine understanding of the influence of elastomer damping treatments as well as a practical know-how in the area of noise reductionAIX-MARSEILLE2-BU Sci.Luminy (130552106) / SudocSudocFranceF

A DETERMINISTIC APPROACH FOR SHAPE AND TOPOLOGY OPTIMISATION UNDER MATERIAL UNCERTAINTY IN ADDITIVE MANUFACTURING

International audienceThe present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and generated by two random variables. These two variables representing the amplitude of the Young’s modulus correspond to the zone of porosity inclusion and surface roughness defects. A deterministic approach that relies on a second-order Taylor expansion of the cost function has been proposed by Allaire & Dapogny [2]. The present work proposes a general framework to handle uncertainties of the Young’s modulus in which its amplitude is divided into N zones and then applied onto two zones corresponding to the porosity inclusion and surface roughness defects. We demonstrate the effectiveness of the approach in the context of the level-set-based topology optimisation for the robust compliance minimisation of three-dimensional cantilever test cases

A DETERMINISTIC APPROACH FOR SHAPE AND TOPOLOGY OPTIMISATION UNDER MATERIAL UNCERTAINTY IN ADDITIVE MANUFACTURING

International audienceThe present work aims at handling uncertain materials in shape and topology optimisation applied to additive manufacturing. More specifically, we minimise an objective function combining the mean values of standard cost functions and assume that the uncertainties are small and generated by two random variables. These two variables representing the amplitude of the Young’s modulus correspond to the zone of porosity inclusion and surface roughness defects. A deterministic approach that relies on a second-order Taylor expansion of the cost function has been proposed by Allaire & Dapogny [2]. The present work proposes a general framework to handle uncertainties of the Young’s modulus in which its amplitude is divided into N zones and then applied onto two zones corresponding to the porosity inclusion and surface roughness defects. We demonstrate the effectiveness of the approach in the context of the level-set-based topology optimisation for the robust compliance minimisation of three-dimensional cantilever test cases