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.

Il ruolo dell'ecografia prenatale nell'infezione congenita da Citomegalovirus

OBJECTIVE: To assess the effectiveness of ultrasound in the antenatal prediction of symptomatic congenital cytomegalovirus infection. STUDY DESIGN: The sonograms of 650 fetuses from mothers with primary cytomegalovirus infection were correlated to fetal/neonatal outcome. Infection status was disclosed by viral urine isolation at birth or CMV tissue inclusions at autopsy. Classification of symptomatic disease was based on postnatal clinical/laboratory findings or macroscopic evidence of tissue damage at autopsy. RESULTS: Ultrasound abnormalities were found in 51/600 (8.5%) mothers with primary infection and in 23/154 congenitally infected fetuses (14.9%). Symptomatic congenital infection resulted in 18/23 and 68/131 cases with or without abnormal sonographic findings, respectively. Positive predictive values of ultrasound versus symptomatic congenital infection was 35.3% relating to all fetuses/infants from mothers with primary infection and 78.3% relating to fetuses/infants with congenital infection. CONCLUSION: When fetal infection status is unknown, ultrasound abnormalities only predict symptomatic congenital infection in a third of cases.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Ottimizzazione di materiali e trattamenti per componenti critici destinati a motociclette da competizione

L’attività svolta durante il dottorato è stata incentrata su due tematiche riguardanti: (i) la modifica della composizione chimica delle classiche leghe di alluminio da fonderia per incrementarne la resistenza e stabilità termica; (ii) lo studio del comportamento a fatica di acciai innovativi alto-resistenziali, allo scopo di valutarne il loro utilizzo per la produzione di alberi motore e distribuzione in sostituzione dei tradizionali acciai utilizzati dopo bonifica e trattamento superficiale di nitrurazione. La messa a punto di una lega di alluminio da fonderia con elevata resistenza in temperatura ha richiesto, oltre all’individuazione della composizione chimica, l’ottimizzazione del trattamento termico e una completa caratterizzazione meccanica statica a fatica sia a temperatura ambiente sia a 200°C. L’attività ha permesso di sviluppare una lega, ottenuta aggiungendo 1,3% in peso di rame alla classica lega A357 (Al-Si-Mg), cha ha mostrato avere proprietà meccaniche superiori a quelle delle tradizionali leghe Al-Si-Mg-Cu quali la A354 e C355 sia a temperatura ambiente che a 200 °C dopo lunga esposizione in temperatura. Per quanto riguarda gli acciai innovativi, dopo una preliminare analisi di mercato per individuare quali acciai potessero essere oggetto di studio, è stato valutato come migliorarne le prestazioni a fatica, anche in presenza d’intaglio, attraverso la scelta del trattamento termico più opportuno e del processo di pallinatura. I risultati delle caratterizzazioni microstrutturale e meccanica svolte hanno permesso di individuare due acciai (nomi commerciali K890 e ASP2017) ottenuti per metallurgia delle polveri, ad oggi utilizzati solo per la produzione di stampi e/o utensili, in grado di sostituire gli acciai con cui vengono oggi realizzati i componenti, senza la necessità di eseguire il trattamento di nitrurazione

Resonant metamaterials for the control of Rayleigh waves

Since their emergence, locally resonant metamaterials have found several applications for the control of surface waves, from micrometer-sized electronic devices to meter-sized seismic barriers. The interaction between Rayleigh-type surface waves and resonant metamaterials has been investigated through the realization of locally resonant metasurfaces, thin elastic interfaces constituted by a cluster of resonant inclusions or oscillators embedded near the surface of an elastic waveguide. When such resonant metasurfaces are embedded in an elastic homogeneous half-space, they can filter out the propagation of Rayleigh waves, creating low-frequency bandgaps at selected frequencies. In the civil engineering context, heavy resonating masses are needed to extend the bandgap frequency width of locally resonant devices, a requirement that limits their practical implementations. In this dissertation, the wave attenuation capabilities of locally resonant metasurfaces have been enriched by proposing (i) tunable metasurfaces to open large frequency bandgaps with small effective inertia, and by developing (ii) an analytical framework aimed at studying the propagation of Rayleigh waves propagation in deep resonant waveguides. In more detail, inertial amplified resonators are exploited to design advanced metasurfaces with a prescribed static and a tunable dynamic response. The modular design of the tunable metasurfaces allows to shift and enlarge low-frequency spectral bandgaps without modifying the total inertia of the metasurface. Besides, an original dispersion law is derived to study the dispersive properties of Rayleigh waves propagating in thick resonant layers made of sub-wavelength resonators. Accordingly, a deep resonant wave barrier of mechanical resonators embedded inside the soil is designed to impede the propagation of seismic surface waves. Numerical models are developed to confirm the analytical dispersion predictions of the tunable metasurface and resonant layer. Finally, a medium-size scale resonant wave barrier is designed according to the soil stratigraphy of a real geophysical scenario to attenuate ground-borne vibration.

Analysis of the main phenomena affecting solid rocket motors internal ballistics

In solid rocket motors, the absence of combustion controllability and the large amount of financial resources involved in full-scale firing tests, increase the importance of numerical simulations in order to asses stringent mission thrust requirements and evaluate the influence of thrust chamber phenomena affecting the grain combustion. Among those phenomena, grain local defects (propellant casting inclusions and debondings), combustion heat accumulation involving pressure peaks (Friedman Curl effect), and case-insulating thermal protection material ablation affect thrust prediction in terms of not negligible deviations with respect to the nominal expected trace. Most of the recent models have proposed a simplified treatment to the problem using empirical corrective functions, with the disadvantages of not fully understanding the physical dynamics and thus of not obtaining predictive results for different configurations of solid rocket motors in a boundary conditions-varied scenario. This work is aimed to introduce different mathematical approaches to model, analyze, and predict the abovementioned phenomena, presenting a detailed physical interpretation based on existing SRMs configurations. Internal ballistics predictions are obtained with an in-house simulation software, where the adoption of a dynamic three-dimensional triangular mesh together with advanced computer graphics methods, allows the previous target to be reached. Numerical procedures are explained in detail. Simulation results are carried out and discussed based on experimental data.

Essays in nonlinear pricing and rent seeking

This thesis consists of three self-contained essays on nonlinear pricing and rent-seeking. In the first chapter of the thesis, I provide new theoretical insights about non-linear pricing in monopoly and common agency by combining the principal-agent framework with other-regarding preferences. I introduce a new theoretical model that separately characterizes status-seeker and inequity-averse buyers. I show how the buyer’s optimal choice of quality and market inefficiency change when the buyer has other-regarding preferences. In the second chapter, I find the optimal productive rent-seeking and sabotaging efforts when the prize is endogenous. I show that due to the existence of endogeneity, sabotaging the productive rent-seeking efforts causes sabotaging the endogenous part of the prize, which can affect the rent-seeking efforts. Moreover, I introduce social preferences into my model and characterize symmetric productive rent-seeking and sabotaging efforts. In the last chapter, I propose a new theoretical model regarding information disclosure with Bayesian persuasion in rent-seeking contests when the efforts are productive. I show that under one-sided incomplete information, information disclosure decision depends on both the marginal costs of efforts and the marginal benefit of aggregate exerted effort. I find that since the efforts are productive and add a positive surplus on the fixed rent, my model narrows down the conditions for the information disclosure compared to the exogenous model. Under the two-sided incomplete information case, I observe that there is a non-monotone relationship between optimal effort and posterior beliefs. Thus, it might be difficult to conclude whether a contest organizer should disclose any information to contestants.