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Les vibrations aléatoires sont les sollicitations les plus représentatives à celles qui se trouvent dans l'environnement réel. Elles sont souvent rencontrées dans l'environnement de fonctionnement automobile, aéronautique, spatial, ferroviaire et d'autres. La particularité des vibrations aléatoires est l'utilisation de son analyse par fatigue. Grâce aux propriétés statistiques des signaux aléatoires que les méthodes spectrales permettent d'estimer la moyenne du dommage d'une façon efficace et économique mais avec certaines limitations. Une étude numérique sur un système électronique embarqué accompagnée des essais expérimentaux ont été mis en place dans cette thèse pour présenter une démarche complète d'une analyse spectrale des vibrations aléatoires. Une modélisation par éléments finis a été réalisée ainsi qu'une technique du 'zoom structural' en analyse spectrale des vibrations aléatoires a été proposée dans ce travail avec la présentation des équations de cette technique. Une application numérique a montré la validité de la technique proposée en appliquant une étude de l'endommagement par fatigue par l'approche temporelle et par l'approche spectrale. Les résultats numériques de cette application mènent à une estimation d'un temps à l'initiation de la fissure très proche du temps de défaillance observé dans les résultats des essais expérimentaux. Cette technique montre la performance et l'efficacité des méthodes spectrales dans l'estimation du dommage par fatigue aléatoire. Une étude de l'optimisation d'un système soumis aux sollicitations aléatoires a été développée. L'objectif de cette étude est de rechercher la conception optimale du système soumis aux vibrations aléatoires en posant des limitations sur le dommage qui en résulte. Ce dommage estimé par les méthodes spectrales de Dirlik et de Single Moment ne doit pas dépasser un dommage cible pour assurer la fiabilité du système étudié. / Random vibrations are the most representative excitations that can be found in the real environment. They are often encountered in the automotive, aeronautical, space, railway and other operating environments. The special feature of the random vibrations is their important role in damage fatigue analysis. The spectral methods allow to estimate efficiently and economically the mean of the damage using the statistical properties of the random signals. A numerical study on an embedded electronic system with experimental tests was set up in this thesis to present a complete spectral analysis of random vibrations methodology. A finite element model was performed as well as submodelling technique in spectral analysis of random vibrations with associated equations was proposed in this work. A numerical application has shown the validity of the proposed technique by applying the fatigue damage study using the time-domain approach and the spectral approach. The numerical results of this application lead to the estimation of a crack initiation time very close to the failure time observed in the experimental tests. This technique shows the performance and efficiency of spectral methods in the estimation of random fatigue damage. The optimization of a system subjected to random excitations has been developed in this work. The objective of this study is to retrieve the optimal design of the system subjected to random vibrations with limitations on the resulting damage. This damage estimated by Dirlik and Single Moment spectral methods must not exceed defined target damage in order to insure the reliability of the studied system.

The scope of this thesis is the design and verification of an electronic packaging of a device which is a subunit of a network system that is designed for combat communication in sheltering ship. According to the project requirements this device is subjected to some environmental and electromagnetic interference tests. This thesis includes design and manufacturing steps as well as vibration, shock and thermal analyses. Electromagnetic interference is examined through the design procedure and total shielding effectiveness of the device is calculated after the applications of some electromagnetic interference precautions which are given in details.

This research study presents a new vibration-based non-destructive global structural damage identification and condition monitoring technique that can be used for detection, localization and quantification of damage. A two-stage damage identification process that combines non-model based and model-based damage identification approaches is proposed to overcome the main difficulties associated with the solution of structural damage identification problems. In the first stage, performance assessment of various response parameters obtained from the time-domain, frequency-domain and spectral-domain analysis is conducted using a non model-based damage detection and localization approach. In addition, vibration response parameters that are sensitive to local and global damage and that possess strong physical relationships with key structural dynamic properties are identified. Moreover, in order to overcome the difficulties associated with damage identification in the presence of structural nonlinearity and response nonstationarity, a wavelet transform based damage-sensitive parameter is presented for detection and localization of damage in the space domain. The level of sensitivity and effectiveness of these parameters for detection and localization of damage are demonstrated using various numerical experimental data determined from one-dimensional and two-dimensional plate-like structures.

A finite element model of the CubeSat MIST was created, in order to assess the stresses that occur in the satellite in response to loads during its launch. Due to size limits of thesoftware used, simplifications had to be made to the geometry of the model. The loads assessed were quasi-static accelerations, random vibrations, shock loads, as well as a combined quasi-static acceleration and random vibration case. The study assumed the worst possible loads from a list of different potential launch vehicles for the satellite. Non-linear boundary conditions could not be modelled, and instead different linear boundary condition combinations were assessed. The results showed that the satellite showed positive margins of safety for the quasi-static loads. The lowest natural frequency for the satellite was above 130 Hz. For the random vibration loads, positive margins of safety could be shown if adverse stresses attributed to the boundary conditions inthe worst case were ignored. The model proved too conservative to qualify the satellite for the shock loads. Shock testing is therefore recommended for future work, unless requirements for waiving the shock testing can be met. The random vibration and combined loads analysis showed that the −X shear panel experienced high stresses in the corners of its windows, and the part should be inspected once environmental tests are conducted. The −X shear panel only showed adverse stresses in the most extreme boundary condition case, where its deformation was deemed unrealistic. / En finit elementmodell av nanosatelliten MIST skapades for att undersöka dess respons till lasterna under uppskjutning. På grund av storleksbegränsningar i programvaran behövde modellens geometri förenklas. Lasterna som undersöktes var kvasistatiska accelerationer, stokastiska vibrationer, chocklaster samt ett kombinerat kvasistatiskt accelerations- och stokastiskt vibrationsfall. Studien använde de värsta tänkbara lasterna från en lista över olika potentiella bärraketer för satelliten. Icke-linjära gränsvillkor kunde inte modelleras och istället utvärderades olika kombinationer av linjära gränsvillkor. Resultaten visade positiva säkerhetsmarginaler för kvasistatiska belastningar. Den lägsta naturliga frekvensen för satelliten var över 130 Hz. För de stokastiska vibrationsbelastningarna kunde positiva säkerhetsmarginaler motiveras om hänsyn togs till oegentligheter orsakade av gränsvillkoren i det extremaste fallet. Chocklastanalysen visade på begränsningar i modellen. Mekaniska chocktester kommer därmed behövas för att undersöka chocklasterna, om inte kraven for att hoppa över chocktestning uppfylls. Analyserna av de stokastiska vibrationerna och det kombinerade lastfallet visade att skjuvpanelen på −X-sidan upplever höga spänningar i hörnen på sina fönster, och bör inspekteras när experimentella tester genomförs. Skjuvpanelen på −X-sidan upplevde enbart för höga spänningar i fallet med mest extrema gröäsvillkor, där deformationerna bedömdes vara orealistiska.

Το πρόβλημα που αντιμετωπίζει η διατριβή αφορά στη μοντελοποίηση μη-στασίμων τυχαίων ταλαντώσεων επί τη βάσει μετρήσεων του σήματος της ταλάντωσης, μέσω μοντέλων FS-TAR/TARMA. Οι στόχοι της διατριβής περιλαμβάνουν την αποτίμηση της εφαρμοσιμότητας των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση της ταλάντωσης χρονικά μεταβαλλόμενών κατασκευών, καθώς και τη σύγκρισή τους με εναλλακτικές παραμετρικές μεθόδους του πεδίου του χρόνου. Ιδιαίτερη βαρύτητα δίνεται και στην αντιμετώπιση θεμάτων που σχετίζονται με την εκτίμηση μοντέλων FS-ΤAR/TARMA, καθώς και στην θεωρητική ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών που χρησιμοποιούνται. Η διατριβή αρχικά παρουσιάζει μια συγκριτική ανασκόπηση της βιβλιογραφίας στο θέμα της μοντελοποίησης μη-στασίμων ταλαντώσεων μέσω παραμετρικών μεθόδων του πεδίου του χρόνου, η οποία και επιδεικνύει τα πλεονεκτήματα των μεθόδων FS-TAR/TARMA. Στη συνέχεια αντιμετωπίζεται μια σειρά προβλημάτων που εμφανίζονται κατά την εκτίμηση (των παραμέτρων) και την επιλογή της δομής του μοντέλου. Η αποτελεσματικότητα των μεθόδων FS-TAR/TARMA για την μοντελοποίηση και ανάλυση μη-στάσίμων ταλαντώσεων επιδεικνύεται και πειραματικά μέσω εφαρμογής στην οποία πραγματοποιείται επιτυχής εξαγωγή των δυναμικών χαρακτηριστικών μιας εργαστηριακής χρονικά μεταβαλλόμενης κατασκευής. Στη συνέχεια, η διατριβή εστιάζει στην αναζήτηση ακριβέστερων εκτιμητριών, καθώς και στην ασυμπτωτική ανάλυση των ιδιοτήτων των εκτιμητριών «γενικών» (όχι αναγκαστικά περιοδικά μεταβαλλόμενων) μοντέλων FS-TAR/TARMA. Συγκεκριμένα, εξετάζονται οι περιπτώσεις των εκτιμητριών σταθμισμένων ελαχίστων τετραγώνων [Weighted Least Squares (WLS)], μέγιστης πιθανοφάνειας [Maximum Likelihood (ML)], καθώς και μια εκτιμήτρια πολλαπλών σταδίων [Multi Stage (MS)], η οποία αναπτύσσεται στην παρούσα διατριβή και είναι ασυμπτωτικά ισοδύναμη με την εκτιμήτρια ML ενώ ταυτόχρονα χαρακτηρίζεται από μειωμένη υπολογιστική πολυπλοκότητα. Στη διατριβή αποδεικνύεται η συνέπεια (consistency) των εκτιμητριών αυτών και εξάγεται η ασυμπτωτική κατανομή (asymptotic distribution) τους. Παράλληλα, αναπτύσσεται μια συνεπής εκτιμήτρια του ασυμπτωτικού πίνακα συνδιασποράς και μια μέθοδος για τον έλεγχο εγκυρότητας των μοντέλων FS-TAR/TARMA. Η ορθότητα των αποτελεσμάτων της ασυμπτωτικής ανάλυσης επιβεβαιώνεται μέσω μελετών Monte Carlo. / The thesis studies the problem of non-stationary random vibration modeling and analysis based on available measurements of the vibration signal via Functional Series Time-dependent AutoRegressive / AutoRegressive Moving Average (FS-TAR/ TARMA) models. The aims of the thesis include the assessment of the applicability of FS-TAR/TARMA methods for the modeling and analysis of non-stationary random vibration, as well as their comparison with alternative time-domain parametric methods. In addition, significant attention has been paid to the FS-TAR/TARMA estimation problem and to the theoretical asymptotic analysis of the estimators. A critical overview and comparison of time-domain, parametric, non-stationary random vibration modeling and analysis methods is firstly presented, where the high potential of FS-TAR/TARMA methods is demonstrated. In the following, a number of issues concerning the FS-TAR/TARMA model (parameter) estimation and model structure selection are considered. The effectiveness of the FS-TARMA methods for non-stationary random vibration modeling and analysis is experimentally demonstrated, through their application for the recovery of the dynamical characteristics of a time-varying bridge-like laboratory structure. In the sequel, the thesis focuses on the asymptotic analysis of “general” (that is not necessarily periodically evolving) FS-TAR/TARMA estimators. In particular, the Weighted Least Squares (WLS) and Maximum Likelihood (ML) estimators are both investigated, while a Multi Stage (MS) estimator, that approximates the ML estimator at reduced complexity, is developed. The consistency of the considered estimators is established and their asymptotic distribution is extracted. Furthermore, a consistent estimator of the asymptotic covariance matrix is formulated and an FS-TAR/TARMA model validation method is proposed. The validity of the theoretical asymptotic analysis results is assessed through several Monte Carlo studies.

Monte Carlo simulation techniques have emerged as widely accepted computing tools in tackling many problems in modern structural mechanics. Apart from developments in computational hardware, which have undoubtedly made simulation strategies practically feasible, the success of Monte Carlo simulations has also resulted equally significantly from the methodological developments aimed at controlling sampling variance of the Monte Carlo estimates. The study reported in the present thesis is aimed at developing and validating Monte Carlo simulation based approaches with inbuilt variance reduction capabilities to deal with problems of time variant reliability modeling, random vibration testing, and updating reliability models for statically/dynamically loaded instrumented structures. The relevant literature has been reviewed in Chapter 1. Time variant reliability analysis of randomly parametered and randomly driven non-linear vibrating systems has been tackled by combining two Monte Carlo variance reduction strategies into a single framework (Chapter 2). The first of these strategies is based on the application of the Girsanov transformation to account for the randomness in dynamic excitations and, the second approach is fashioned after the subset simulation method to deal with randomness in system parameters. A novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models has been proposed (Chapter 3). The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov’s transformation. The study observes that an acceptable choice for the control force (that can reduce the sampling variance of the estimator) can be made solely based on experimental techniques. This permits the proposed procedure to be applied in the experimental study of time variant reliability of complex structural systems which are difficult to model mathematically. Illustrative example consists of a multi-axes shake table study on bending-torsion coupled, geometrically non-linear, five-storey frame under uni/bi-axial, non-stationary, random base excitation. The first order reliability method (FORM) and inverse FORM have been extended to handle the problem of updating reliability models for existing, statically loaded structures based on measured responses (Chapter 4). The proposed procedures are implemented by combining Matlab based reliability modules with finite element models residing on the Abaqus software. Numerical illustrations on linear and non-linear frames are presented. A solution strategy within the framework of Monte Carlo simulation based dynamic state estimation method and Girsanov’s transformation for variance reduction has been developed to tackle the problem of updating the reliability of instrumented structures based on measured response under random dynamic loading (Chapter 5). For linear Gaussian state space models, the solution is developed based on continuous version of the Kalman filter, while, for non-linear and (or) non-Gaussian state space models, bootstrap particle filters are adopted. Results from laboratory testing of an archetypal five storey bending-torsion coupled frame under seismic base motions form the basis of one of the illustrative examples. A set of three annexures contain details of numerical methods for discretizing Ito’s differential equations (Annexure 1), working of the Girsanov transformation through Kolmogorov’s equations (Annexure 2) and tools for interfacing Matlab and Abaqus codes (Annexure 3).