Prediction and measurement of forced response of a composite blade undergoing nonlinear vibration

The main objective of this project is to experimentally demonstrate geometrical nonlinear phenomena due to large displacements during resonant vibration of composite materials and to explain the problem associated with fatigue prediction at resonant conditions. Three different composite blades to be tested were designed and manufactured, being their difference in the composite layup (i.e. unidirectional, cross-ply, and angle-ply layups). Manual envelope bagging technique is explained as applied to the actual manufacturing of the components; problems encountered and their solutions are detailed. Forced response tests of the first flexural, first torsional, and second flexural modes were performed by means of a uniquely contactless excitation system which induced vibration by using a pulsed airflow. Vibration intensity was acquired by means of Polytec LDV system. The first flexural mode is found to be completely linear irrespective of the vibration amplitude. The first torsional mode exhibits a general nonlinear softening behaviour which is interestingly coupled with a hardening behaviour for the unidirectional layup. The second flexural mode has a hardening nonlinear behaviour for either the unidirectional and angle-ply blade, whereas it is slightly softening for the cross-ply layup. By using the same equipment as that used for forced response analyses, free decay tests were performed at different airflow intensities. Discrete Fourier Trasform over the entire decay and Sliding DFT were computed so as to visualise the presence of nonlinear superharmonics in the decay signal and when they were damped out from the vibration over the decay time. Linear modes exhibit an exponential decay, while nonlinearities are associated with a dry-friction damping phenomenon which tends to increase with increasing amplitude. Damping ratio is derived from logarithmic decrement for the exponential branch of the decay.

La metrica di Agmon ed il decadimento esponenziale delle soluzioni di equazioni alle derivate parziali

The aim of this master thesis is to study the exponential decay of solutions of elliptic partial equations. This work is based on the results obtained by Agmon. To this purpose, first, we define the Agmon metric, that plays an important role in the study of exponential decay, because it is related to the rate of decay. Under some assumptions on the growth of the function and on the positivity of the quadratic form associated to the operator, a first result of exponential decay is presented. This result is then applied to show the exponential decay of eigenfunctions with eigenvalues whose real part lies below the bottom of the essential spectrum. Finally, three examples are given: the harmonic oscillator, the hydrogen atom and a Schrödinger operator with purely discrete spectrum.

Dupire's formula for exponential Lévy models

Questa tesi è incentrata sull'analisi della formula di Dupire, che permette di ottenere un'espressione della volatilità locale, nei modelli di Lévy esponenziali. Vengono studiati i modelli di mercato Merton, Kou e Variance Gamma dimostrando che quando si è off the money la volatilità locale tende ad infinito per il tempo di maturità delle opzioni che tende a zero. In particolare viene proposta una procedura di regolarizzazione tale per cui il processo di volatilità locale di Dupire ricrea i corretti prezzi delle opzioni anche quando si ha la presenza di salti. Infine tale risultato viene provato numericamente risolvendo il problema di Cauchy per i prezzi delle opzioni.

PM and material decay: analysis of dry depositions on horizontal and vertical surrogate surfaces through a Deposition Box system

Airborne Particulate Matter (PM), can get removed from the atmosphere through wet and dry mechanisms, and physically/chemically interact with materials and induce premature decay. The effect of dry depositions is a complex issue, especially for outdoor materials, because of the difficulties to collect atmospheric deposits repeatable in terms of mass and homogeneously distributed on the entire investigated substrate. In this work, to overcome these problems by eliminating the variability induced by outdoor removal mechanisms (e.g. winds and rainfalls), a new sampling system called ‘Deposition Box’, was used for PM sampling. Four surrogate materials (Cellulose Acetate, Regenerated Cellulose, Cellulose Nitrate and Aluminum) with different surfaces features were exposed in the urban-marine site of Rimini (Italy), in vertical and horizontal orientations. Homogeneous and reproducible PM deposits were obtained and different analytical techniques (IC, AAS, TOC, VP-SEM-EDX, Vis-Spectrophotometry) were employed to characterize their mass, dimension and composition. Results allowed to discriminate the mechanisms responsible of the dry deposition of atmospheric particles on surfaces with different nature and orientation and to determine which chemical species, and in which amount, tend to preferentially deposit on them. This work demonstrated that “Deposition Box” can represent an affordable tool to study dry deposition fluxes on materials and results obtained will be fundamental in order to extend this kind of exposure to actual building and heritage materials, to investigate the PM contribution in their decay.