A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

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.

Vibro-acoustic analysis of additively manufactured acoustic metamaterials

In the last decade it emerged the interest in new types of acoustic insulating materials, called acoustic metamaterials. These materials are composed by a host and inclusions and are arranged periodically or non-periodically in sub-wavelength elements called meta-atoms. Their inclusions and internal geometries can be manipulated to tailor the acoustic properties, reducing weight, and increasing at the same time their efficiency. Thanks to the high absorbing characteristics that they can achieve, their usage is of particularly interest as material of the core in sandwich panels of aerospace structures to reduce vibrations and noise inside passengers aircraft’s cabin. In addition, since the low frequency signals are difficult to be damped with conventional materials, their usage can guarantee a high transmission loss at low frequencies, obtaining a positive benefit on passengers’ comfort. The performances and efficiency of these materials are enhanced thanks to the new additive manufacturing techniques opposed to the conventional ones uncapable to pro- duce such complex internal geometries. The aim of this work is to study, produce and redesign micro-perforated sandwich panels of a literature case study to achieve high performances in the low frequency range, e.g., below 2000 Hz. Some geometrical parameters, such as perforation ratio and diameter of holes, were considered to realize different models and see the differences in the sound transmission loss. The models were produced by means of Fused Deposition Modelling using an Acrylonitrile Butadiene Styrene (ABS Plus p430) material on a commercial additive manufacturing system. Finally, the frequency response analysis was carried out with Mul2 software, based on the Carrera’s Unified Formulation (CUF) to understand the acoustic and structural properties of the material employed, analyzing the plates’ displacements and the TL results.

Mitigation of Train-Induced waves by resonant filled-trench (RFT)

The increase of railways near the urban areas is a significant cause of discomfort for inhabitants due to train-induced vibration and noise. Vibration characteristics can vary widely according to the train type: for high-speed trains, if train speed becomes comparable to the ground wave speed, the vibration level becomes significant; for freight trains, due to their heavier weight and lower speed, the vibration amplitudes are greater and propagate at a more considerable distance from the track; for urban tramways, although the vibration amplitude is relatively low, they can have a negative structural effect on the closest buildings [51]. Therefore, to dampen the vibration level, it is possible to carry out some interventions both on the track and the transmission path. This thesis aims to propose and numerically investigate a novel method to dampen the train-induced vibrations along the transmission path. The method is called "resonant filled-trench (RFT)" and consists of a combination of expanded polystyrene (EPS) geofoam to stabilize the trench wall against the collapse and drowned cylindrical embedded inclusions inside the geofoam, which act as a resonator, reflector, and attenuator. By means of finite element simulations, we show that up to 50% higher attenuation than the open trench is achievable after overcoming the resonance frequency of the inclusion, i.e., 35Hz, which covers the frequency contents of the train-induced vibration. Moreover, depending on the filling material used for the inclusions, trench depth can be reduced up to 17% compared to the open trench showing the same screening performance as the open trench. Also, an RFT with DS inclusion installed in dense sand soil shows a high hindrance performance (i.e., IL≥6dB) when the trench depth is larger than 0.5λ_R while it is 0.6λ_R for the open trench.

Mineral paragenesis and fluid inclusion constraints on the Torre di Rio skarn, Island of Elba

The historical iron ore deposits of eastern Elba held great importance for the region and were its primary source of iron. The Torre di Rio skarn, despite its easily accessible outcrop and vicinity to the larger Rio Marina deposit, was never properly characterized. The results of petrographic and microthermometric study presented in this work provide new constraints on the Torre di Rio skarn. Mineral assemblage of ilvaite, calcite, quartz, iron oxides and sulphides combined with textural evidence indicate that Torre di Rio skarn does not fit into classical skarn model. The complex paragenetic sequence and overlapping of skarn and ore mineralogy is result of fast formation at relatively low temperatures evidenced by the silicon enrichment and pervasive nature of limonite alteration. Hematite-magnetite textural relationship points to boundary conditions of the ore fluid in terms of oxygen fugacity. Eutectic temperatures range from -16 to -33 °C indicating complex fluids. Calculated salinities range from 1.4 to 17.4 wt% NaCleq suggesting multiple fluids of different compositions. Total homogenization temperatures vary from 330 °C to 150 °C with both homogeneously and heterogeneously trapped FIAs. Ore deposition is concentrated where skarn formation was controlled primarily by phase separation during boiling. Calculated fluid pressure at boiling suggest shallow formation depth of a few hundred meters and constrains maximum temperature of ore deposition to c. 260 °C. This work suggest that relatively low salinities of fluid inclusions could indicate dominant marine origin of the hydrothermal fluids that were activated by the Porto Azzurro pluton emplacement and that scavenged Fe from sedimentary host rocks. During boiling at shallow depths and decreasing iron solubility, these fluids started precipitating Fe-minerals at Torre di Rio mineralization. Mixing with batches of more saline fluids at around 236 °C increased salinity abruptly and marked the end of ore deposition.