Numerical and analytical vibro-acoustic modelling of porous materials: the Cell Method for poroelasticity and the case of inclusions

Porous materials are widely used in many fields of industrial applications, to achieve the requirements of noise reduction, that nowadays derive from strict regulations. The modeling of porous materials is still a problematic issue. Numerical simulations are often problematic in case of real complex geometries, especially in terms of computational times and convergence. At the same time, analytical models, even if partly limited by restrictive simplificative hypotheses, represent a powerful instrument to capture quickly the physics of the problem and general trends. In this context, a recently developed numerical method, called the Cell Method, is described, is presented in the case of the Biot's theory and applied for representative cases. The peculiarity of the Cell Method is that it allows for a direct algebraic and geometrical discretization of the field equations, without any reduction to a weak integral form. Then, the second part of the thesis presents the case of interaction between two poroelastic materials under the context of double porosity. The idea of using periodically repeated inclusions of a second porous material into a layer composed by an original material is described. In particular, the problem is addressed considering the efficiency of the analytical method. A analytical procedure for the simulation of heterogeneous layers based is described and validated considering both conditions of absorption and transmission; a comparison with the available numerical methods is performed. ---------------- I materiali porosi sono ampiamente utilizzati per diverse applicazioni industriali, al fine di raggiungere gli obiettivi di riduzione del rumore, che sono resi impegnativi da norme al giorno d'oggi sempre più stringenti. La modellazione dei materiali porori per applicazioni vibro-acustiche rapprensenta un aspetto di una certa complessità. Le simulazioni numeriche sono spesso problematiche quando siano coinvolte geometrie di pezzi reali, in particolare riguardo i tempi computazionali e la convergenza. Allo stesso tempo, i modelli analitici, anche se parzialmente limitati a causa di ipotesi semplificative che ne restringono l'ambito di utilizzo, rappresentano uno strumento molto utile per comprendere rapidamente la fisica del problema e individuare tendenze generali. In questo contesto, un metodo numerico recentemente sviluppato, il Metodo delle Celle, viene descritto, implementato nel caso della teoria di Biot per la poroelasticità e applicato a casi rappresentativi. La peculiarità del Metodo delle Celle consiste nella discretizzazione diretta algebrica e geometrica delle equazioni di campo, senza alcuna riduzione a forme integrali deboli. Successivamente, nella seconda parte della tesi viene presentato il caso delle interazioni tra due materiali poroelastici a contatto, nel contesto dei materiali a doppia porosità. Viene descritta l'idea di utilizzare inclusioni periodicamente ripetute di un secondo materiale poroso all'interno di un layer a sua volta poroso. In particolare, il problema è studiando il metodo analitico e la sua efficienza. Una procedura analitica per il calcolo di strati eterogenei di materiale viene descritta e validata considerando sia condizioni di assorbimento, sia di trasmissione; viene effettuata una comparazione con i metodi numerici a disposizione.

El Niño southern oscillation and its effect on fog oases along the Peruvian and Chilean coastal deserts

Fog oases, locally named Lomas, are distributed in a fragmented way along the western coast of Chile and Peru (South America) between ~6°S and 30°S following an altitudinal gradient determined by a fog layer. This fragmentation has been attributed to the hyper aridity of the desert. However, periodically climatic events influence the ‘normal seasonality’ of this ecosystem through a higher than average water input that triggers plant responses (e.g. primary productivity and phenology). The impact of the climatic oscillation may vary according to the season (wet/dry). This thesis evaluates the potential effect of climate oscillations, such as El Niño Southern Oscillation (ENSO), through the analysis of vegetation of this ecosystem following different approaches: Chapters two and three show the analysis of fog oasis along the Peruvian and Chilean deserts. The objectives are: 1) to explain the floristic connection of fog oases analysing their taxa composition differences and the phylogenetic affinities among them, 2) to explore the climate variables related to ENSO which likely affect fog production, and the responses of Lomas vegetation (composition, productivity, distribution) to climate patterns during ENSO events. Chapters four and five describe a fog-oasis in southern Peru during the 2008-2010 period. The objectives are: 3) to describe and create a new vegetation map of the Lomas vegetation using remote sensing analysis supported by field survey data, and 4) to identify the vegetation change during the dry season. The first part of our results show that: 1) there are three significantly different groups of Lomas (Northern Peru, Southern Peru, and Chile) with a significant phylogenetic divergence among them. The species composition reveals a latitudinal gradient of plant assemblages. The species origin, growth-forms typologies, and geographic position also reinforce the differences among groups. 2) Contradictory results have emerged from studies of low-cloud anomalies and the fog-collection during El Niño (EN). EN increases water availability in fog oases when fog should be less frequent due to the reduction of low-clouds amount and stratocumulus. Because a minor role of fog during EN is expected, it is likely that measurements of fog-water collection during EN are considering drizzle and fog at the same time. Although recent studies on fog oases have shown some relationship with the ENSO, responses of vegetation have been largely based on descriptive data, the absence of large temporal records limit the establishment of a direct relationship with climatic oscillations. The second part of the results show that: 3) five different classes of different spectral values correspond to the main land cover of Lomas using a Vegetation Index (VI). The study case is characterised by shrubs and trees with variable cover (dense, semi-dense and open). A secondary area is covered by small shrubs where the dominant tree species is not present. The cacti area and the old terraces with open vegetation were not identified with the VI. Agriculture is present in the area. Finally, 4) contrary to the dry season of 2008 and 2009 years, a higher VI was obtained during the dry season of 2010. The VI increased up to three times their average value, showing a clear spectral signal change, which coincided with the ENSO event of that period.