Vibroacoustics of Periodic Structures. Model Order Reduction, Characterization, Optimization

Noise pollution has been identified as a physiological stressor that impacts both the physiological and psychological health of those exposed to it. This recognition has motivated the imposition of stricter noise regulations which justify the increasing importance of vibroacoustic performance in a broad range of industries that includes the automotive, aerospace, building, and home appliance industries. However, the need and demand for better acoustic comfort often conflict with other design imperatives such as compactness, cost, weight, or ecological targets. Notably, an easy way to increase the vibroacoustic performance of a structure is to increase its mass which, because it requires the use of more material, impacts all the aforementioned targets. In the past decades, the technical challenges induced by higher vibroacoustics standards have been answered by combining stiff, lightweight materials such as aluminum with so-called "vibroacoustic packages" including viscoelastic and poroelastic materials known for their respective abilities to dissipate vibration and acoustic energy. Recently, periodic structures and metamaterials have emerged as a possible, complementary way to achieve better vibroacoustic performance as they often possess unconventional wave propagation properties caused by their multi-scale nature. As a result, they have been the focus of intensive research aimed at understanding their phenomenology and leveraging it in novel vibroacoustic designs. Three challenges to the realization of the aforementioned research program are identified and constitute the main focus of this thesis. Firstly, the computational cost associated with the modeling of metamaterial solutions. Secondly, the absence of a well-established optimization framework for the optimization of metamaterials that accounts for the specificities of the multi-scale/spectral methods developed to model them. Lastly, the difficulty to compare experimental results with numerical models as multiscale methods predict indicators that are not easily measured or estimated (e.g. wavenumbers). To reduce the computational cost associated with the modeling of metamaterials, two model order reduction schemes are developed. The first one concerns the free and forced wave propagation in periodic media and combines mode-based and wave-based reduction methods. The proposed scheme is compared to other techniques presented in the literature and is shown to perform favorably. The second method is based on a multiparameter moment matching technique and is developed to speed up sound transmission loss computations in the shift cell operator method. A reduction of CPU time by up to three orders of magnitude is observed. Regarding optimization, a framework for the unit-cell modeling of periodic structures and metamaterials is developed. The proposed framework combines semi-analytical derivatives of objectives functions computed through unit-cell methods with a second-order optimization algorithm. The aforementioned algorithm is an instance of sequential quadratic programming that combines a line search method (used when the optimization function is locally convex) and an ellipsoidal trust-region method. The proposed framework is applied to model updating, sound transmission loss, and vibration-based problems and produces effective solutions in all cases. Concerning the experimental characterization of periodic media, a novel wavenumber extraction method is developed. The proposed method requires periodic sampling of the signal of interest to produce a convolution kernel that describes its wavenumbers or k-space. In this work, the proposed method is compared to other wavenumber extraction techniques presented in the literature and outperforms them in terms of speed and accuracy.

Jaar van publicatie:2021

Toegankelijkheid:Closed