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AMS Dottorato Alma Mater Studiorum - Università di Bologna Facoltà di Ingegneria - DISTART Dottorato di Ricerca in SCIENZE GEODETICHE E TOPOGRAFICHE Raggruppamento disciplinare ICAR 06 STUDIO DELLE DEFORMAZIONI GRAVITAZIONALI DELLE ANTENNE VLBI DI MEDICINA E DI NOTO CON METODOLOGIE LASER SCANNING, TOPOGRAFICHE E FEM Tesi di Dottorato di: Tutori: Ing. Simonetta Montaguti Prof. Luca Vittuari Dott. Pierguido Sarti Coordinatore: Prof. Gabriele Bitelli XX Ciclo QUESTA TESI E’ STATA SVOLTA NELL’AMBITO DELLE ATTIVITA’ DI RICERCA FINANZIATE DALL’ISTITUTO DI RADIOASTRONOMIA DELL’ISTITUTO NAZIONALE DI ASTROFISICA DI BOLOGNA Parole chiave PAROLE CHIAVE ANTENNE VLBI DEFORMAZIONI GRAVITAZIONALI LASER SCANNING GEODESIA CLASSICA ELEMENTI FINITI Indice INDICE Introduzione 1 1. VLBI ( Very Long Baseline Interferometry) 5 1.1 Introduzione alla interferometria radio 5 1.1.1 La tecnica VLBI 9 1.1.2 Applicazioni della tecnica VLBI 15 1.2 Radiotelescopi di Medicina e di Noto 20 1.2.1 Tipologie dei radiotelescopi 26 1.2.2 Punto di riferimento delle tecniche geodetiche spaziali 28 1.2.3 Deformazioni strutturali delle antenne VLBI 32 2. Tecniche integrate laser scanning e topografiche per la misura delle deformazioni gravitazionali delle antenne VLBI di Medicina e di Noto 37 2.1 Introduzione ai sistemi laser scanner terrestri 37 2.1.1 Principi di acquisizione 39 2.1.2 Procedure di rilievo e data processing 44 2.2 Indagini laser realizzate presso i radiotelescopi di Medicina e di Noto 46 2.3 Considerazioni pratiche ed operative sulle procedure di rilievo topografiche 49 2.4 Indagini topografiche realizzate presso i radiotelescopi di Medicina e di Noto 52 3. FEM ( Finite Element Method) 57 3.1 Introduzione ai modelli numerici 57 3.1.1 Presentazione del metodo 58 3.1.2 Proprietà del metodo 62 i Indice 3.2 Modello agli elementi finiti realizzato per il radiotelescopio di Medicina 72 4. Analisi e confronti fra le diverse metodologie 81 4.1 Post-processing dei dati laser e relativi risultati 81 4.1.1 Codice realizzato in Fortran 90 per la stima del paraboloide di best-fit 97 4.2 Post-processing dei dati topografici e relativi risultati 102 4.3 Deformazioni gravitazionali del riflettore primario dei telescopi VLBI: laser scanning e FEM a confronto 107 4.4 Deformazioni gravitazionali del quadrupode dei telescopi VLBI: osservazioni topografiche e FEM a confronto 114 Conclusioni 120 Bibliografia 124 Appendice A Nodal solution: output dell’elaborazione Ansys per il modello matematico alla elevazione di 90° 131 ii Introduzione INTRODUZIONE Le antenne paraboliche di Medicina (BO) e di Noto (SR) sono dei telescopi realizzati nell'ambito del progetto nazionale VLBI (Very Long Baseline Interferometry ), per operare in collegamento con altri radiotelescopi esteri, sfruttando la tecnica interferometrica a lunga base (Sovers et al. 1998, Thompson et al. 2001). Tali antenne, in particolare, fanno parte delle reti europee per l'astronomia, EVN (European VLBI Network ) e per la Geodesia e, in quest’ultimo settore, partecipano ai programmi osservativi gestiti e coordinati dall’International VLBI Service for Geodesy and Astrometry , IVS (http://ivscc.gsfc.nasa.gov/). Negli ultimi anni, l’attenzione della comunità geodetica internazionale si è concentrata sulla necessità di realizzare misure di alta precisione dei vettori eccentricità tra i punti di riferimento delle diverse tecniche geodetiche co-locate presso il medesimo osservatorio. Quest’approccio, oltre a garantire un effettivo apporto delle local ties in sede di compensazione ITRF (Altamimi et. al. 2002, Altamimi et. al. 2005, Altamimi et. al. 2007) e per gli altri parametri combinati (e.g. Kruegel et al. 2007, Thaller et al. 2007), permette di valorizzare il ruolo degli osservatori geodetici multi-tecnica anche nelle applicazioni a scala nazionale, regionale e locale. In particolare, la possibilità di collegare i punti di riferimento di tecniche, quali VLBI, SLR ( Satellite Laser Ranging ), DORIS ( Doppler Orbitography Radiopositioning Integrated by Satellite ) e GPS ( Global Positioning System ), a reti terrestri consente l’inquadramento di reti locali, anche di carattere tecnico, nel sistema di riferimento internazionale (Sarti e Vittuari 2004). Gli osservatori di Medicina e di Noto sono entrambi dei siti co- locati ITRF dove i vettori eccentricità fra le due tecniche presenti, GPS-VLBI, vengono regolarmente rilevati utilizzando un metodo 1 Introduzione indiretto basato su osservazioni terrestri di elevata precisione (Sarti et al. 2004). Entrambe le local ties , rilasciate nel formato SINEX (Solution Independent Exchange format ) con la rigorosa matrice di varianza e covarianza, sono state utilizzate nel più recente calcolo del sistema di riferimento internazionale terrestre: ITRF2005 (Altamimi et al. 2007). Diverse sono le cause che possono influenzare la precisione nella stima delle eccentricità: la stabilità dei punti di riferimento dei diversi strumenti geodetici spaziali co-locati riveste un ruolo fondamentale. La posizione teorica del reference point è ben definita per ogni strumento geodetico spaziale (Sarti e Angermann 2005) ma la sua realizzazione fisica potrebbe subire notevoli variazioni a causa della gravità e dei gradienti termici che tendono a modificare la struttura del telescopio VLBI. Modelli di deformazione dipendenti dalla temperatura sono attualmente in fase di definizione allo scopo di valutare l’influenza delle variazioni termiche durante le osservazioni (Nothnagel et al. 1995, Wresnik et al. 2007). Difficilmente modellabili risultano invece le deformazioni gravitazionali che tendono a degradare le osservazioni geodetiche VLBI e a diminuire l'accuratezza dei parametri geodetici stimati (Carter et al. 1980). I metodi indiretti per la stima del punto di riferimento, basati su osservazioni terrestri di targets distribuiti sulla struttura esterna del radiotelescopio, possono fornire importanti informazioni riguardanti le deformazioni di alcune parti della struttura del telescopio ma non sono in grado di descrivere completamente la variazione del percorso del segnale VLBI dovuto alle deformazioni gravitazionali. Al fine di creare un modello di elevazione che tenga conto delle variazioni del percorso del segnale indotte dalla gravità occorre determinare la variazione di posizione dei ricevitori, lo scivolamento del dish e le variazioni della distanza focale (Clark e Thomsen 1988). 2 Introduzione Nei telescopi VLBI le variazioni della distanza focale sono direttamente legate alle deformazioni della specchio primario (paragrafo 1.2-3). Nel settembre del 2005, la forma del riflettore primario delle antenne VLBI di Medicina e di Noto, a differenti elevazioni (90°, 75°, 60°, 45°, 30°, 15°), è stata da noi direttamente determinata mediante un’indagine laser di tipo terrestre. Il sistema laser utilizzato, Trimble- Mensi GS200 (http://www.trimble.com/gs200.shtml), è stato posizionato in prossimità del fuoco secondario, su due supporti creati ad hoc per questo tipo di indagine e la distanza focale, nonché gli altri parametri geometrici del paraboloide, sono stati stimati utilizzando un approccio best-fit applicato alle nuvole di punti acquisite. L’indagine laser è stata integrata con osservazioni terrestri realizzate da due total stations di alta precisione; TDA5005 (15 mgon; 1 millimetro + 2 ppm), TC2003 (0,15 mgon; 1 millimetro + 1ppm). In particolare, le indagini topografiche hanno permesso l’inserimento delle nuvole laser all’interno dello stesso sistema topocentrico utilizzato per la stima delle local ties . Inoltre, grazie alle campagne di misura realizzate nel mese di ottobre 2006, presso l’osservatorio di Medicina, e nel mese di agosto 2007 in entrambi i telescopi VLBI di Medicina e di Noto, è stato possibile valutare le deformazioni gravitazionali del quadrupode. Infine, per poter confrontare e confermare le deformazioni gravitazionali del riflettore primario e del quadrupode, ricavate dalle indagini laser e topografiche, un modello agli elementi finiti è stato applicato all’antenna di Medicina. Di seguito viene brevemente illustrata la struttura attraverso la quale si articolerà la presente tesi. Capitolo 1. Breve introduzione alla interferometria radio fino a giungere alla descrizione della tecnica interferometrica ad elementi disconnessi ( Very Long Baseline Interferometry ) e alle sue principali 3 Introduzione applicazioni soprattutto in campo geodetico. Descrizione delle caratteristiche geometriche e tecniche delle antenne VLBI di Medicina e di Noto, delle loro differenze e delle deformazioni strutturali a cui esse possono essere soggette. Definizione dei reference points per le principali tecniche geodetiche spaziali e breve illustrazione del procedimento indiretto utilizzato per determinare l’ invariant point per la tecnica VLBI. Capitolo 2. Considerazioni pratiche ed operative sulle procedure di rilievo utilizzate per lo studio delle deformazioni gravitazionali dei radiotelescopi di Medicina e di Noto ( laser scanning terrestre e topografia). Descrizione di tutte le operazioni, le soluzioni tecniche, gli accorgimenti adottati in entrambe la campagne di misura e le problematiche incontrate. Capitolo 3. Illustrazione dei concetti di base e delle caratteristiche generali su cui si fonda il metodo di analisi strutturale agli elementi finiti e delle fasi fondamentali attraverso le quali si esplica l’analisi stessa con questo tipo di approccio. Descrizione di tutti gli schemi strutturali agli elementi finiti, delle condizioni di carico e di vincolo adottate nel modello dell’antenna VLBI di Medicina. Capitolo
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