Η παρούσα διδακτορική διατριβή αναπτύσσεται ο υδροδυναμικός και δομικός (μηχανολογικός) σχεδιασμός μιας υποθαλάσσιας κατασκευής για την απάντληση πετρελαίου σε μεγάλα βάθη. Η κατασκευή αποτελείταια από 6 διαφορετικά τμήματα. Ο μηχανολογικός σχεδιασμός ξεκίνησε με την προσαρμογή κατάλληλων προδιαγραφών για το κάθε εξάρτημα. Το πρώτο εξάρτημα από το οποίο ξεκίνησε η ανάλυση είναι τα καλώδια ενίσχυσης των οποίων το φορτίο προέντασης είναι ήδη γνωστό από τα κριτήρια σχεδιασμού και τον αρχικό σχεδιασμό και περιορίζεται στους 1000 τόνους (10000 kN). Πραγματοποιήθηκε η τελική επιλογή του υλικού και των χαρακτηριστικών που έπρεπε να έχει ώστε να ανταποκρίνεται στις απαιτήσεις του θαλάσσιου περιβάλλοντος. Ο κατακόρυφος αγωγός με βάση την φιλοσοφία ανάπτυξης του συστήματος θα έπρεπε να αποτελείται από επιμέρους τμήματα αγωγών πεπερασμένου μήκους, κατασκευασμένους από πολυαιθυλένιο οι οποίοι καλύπτουν το συνολικό επιχειρησιακό βάθος. Η αλληλεπίδραση του θαλασσίου ρεύματος με τον αγωγό (Fluid Structure Interaction) για την κάθε διαφορετική ταχύτητα του θαλασσίου προφίλ ώστε να αποφευχθεί η πιθανότητα εμφάνισης επαγώμενων στροβίλων που θα μπορούσαν να οδηγήσουν σε ανεπιθύμητες ταλαντώσεις και σε κόπωση (Vortex Induced Vibration, VIV) τέθηκε σε πρώτη πρωτεραιότητα. Ο συνδυασμός αναλυτικών σχέσεων και πειραματικών δεδομένων από την βιβλιογραφία χρησιμοποιήθηκαν για να υπολογιστεί το μήκος των επιμέρους τμημάτων των αγωγών ώστε να περιοριστούν οι υψηλές εγκάρσιες μετατοπίσεις λόγω των ταλαντώσεων. Η μελέτη της διφασικής ροής πετρελαίου/ νερού σε κώδικα πεπερασμένων όγκων (FLUENT) πραγματοποιήθηκε τόσο για κατακόρυφη όσο και για κεκλιμένη θέση του αγωγού για να επιβεβαιωθεί ότι το αργό πετρέλαιο διατηρεί ανωστική πορεία προς την επιφάνεια ξεπερνώντας τις δυνάμεις τριβής που αναπτύσσονται λόγω της επαφής με τα τοιχώματα των αγωγών. Η ταχύτητα του μίγματος της εσωτερικής ροής καταγράφεται ώστε να ελεγχθεί η εσωτερική μεταβολή της πίεσης του αγωγού. Πιθανή υψηλή διαφοροποίηση της υδροστατικής πίεσης στο εσωτερικό του αγωγού σε σχέση με το εξωτερικό θα οδηγούσε σε επιπλέον φορτία στην δομή του αγωγού (ο αγωγός θα λειτουργούσε τοπικά ως πιεστικό δοχείο). Η προσομοίωση της εξωτερικής ροής γύρω από τμήμα του αγωγού με τα καλώδια ενίσχυσης τοποθετημένα στην περιφερειά του σε κώδικα πεπερασμένων όγκων FLUENT πραγματοποιήθηκε για τον προσδιορισμό των υδροδυναμικών συντελεστών στο εύρος ταχυτήτων 0.1-0.7 m/sec. Επίσης η μοντέλοποίηση αυτή έδειξε κατά πόσο η θέση των νημάτων επιρεάζει ή όχι την δημιουργία επαγώμενων στροβίλων γύρω από τον αγωγό. Η δομική ανάλυση με χρήση πακέτου πακέτου πεπερασμένων στοιχείων (NASTRAN/ PATRAN) έδειξε τα επίπεδα των μέγιστων τάσεων και μετατοπίσεων που αναπτύσσονται λόγω της ύπαρξης της δυναμικής πίεσης η οποία και καταπονεί τοπικά τους αγωγούς. Η αποθηκευτική δεξαμενή (πλωτήρας και συλλέκτης) σχεδιάστηκε με χρήση βασικών υπολογισμών ώστε να επιτευχθεί η κατάλληλη χωρητικότητα αλλά και η προδεγεγραμμένη άνωση. Ο προσδιορισμός των υδροδυναμικών συντελεστών πραγματοποιήθηκε σε FLUENT έτσι ώστε να διερευνηθεί το ροικό πεδίο γύρω από την δεξαμενή καθώς και το μέγεθος των δυνάμεων που μεταφέρονται στο σύστημα από την αλληλεπιδρασή της με το θαλάσσιο ρεύμα. Η δομή του πλωτήρα σχεδιάστηκε με χρήση βασικών δομικών υπολογισμών και η συνολική του συμπεριφορά κάτω από τα φορτία υδροστατικής πίεσης ελέγχθηκε με πεπερασμένα στοιχεία (NASTRAN/ PATRAN). Η δομή του συλλέκτη διαστασιολογήθηκε με βάση την επίδραση της δυναμικής πίεσης ένεκα της ροής γύρω του. Επίσης παρατίθονται οι βασικές δομικές αναλύσεις των συνδέσμων που χρησιμοποιήθηκαν για την ένωση των διαφόρων τμημάτων πλωτήρα και συλλέκτη. Το μοντέλο πλήρους κλίμακας αναπτύχθηκε με βάση τα πειράματα της υδροσήραγγας που πραγματοποιήθηκαν στην MARIN και με βάση του μοντέλου δυναμικής απόκρισης που δημιουργήθηκε στο ORCAFLEX από την SIREHNA. Σκοπός του μοντέλου πλήρους κλίμακας (με την χρήση NASTRAN/PATRAN) ήταν να εξομοιώσει την απόκριση του μοντέλου του ORCAFLEX το οποίο είχε ρυθμιστεί με βάση την υδροσήραγγα ώστε να υπολογιστούν οι δυνάμεις που μεταφέρονται στους δακτυλίους ενίσχυσης και τα φορτία (δυνάμεις και ροπές) που μεταφέρονται στο ενδιάμεσο στοιχείο. Τα δύο μοντέλα θα έπρεπε να εμφανίζουν την ίδια μέγιστη μετατόπιση ώστε να θεωρηθούν όμοια. Στην φάση αυτή τα καλώδια ενίσχυσης που μοντελοποιούνται με μονοδιάστατα στοιχεία στο NASTRAN/PATRAN . Το ενδιάμεσο στοιχείο αποτέλεσε το εξάρτημα στο οποίο μεταφέρονται τα φορτία του αγωγού στο σημείο σύνδεσης (δυνάμεις και οι ροπές) καθώς και οι δυνάμεις από τα καλώδια ενίσχυσης. Η δομική του ανάλυση περιλαμβάνει την διαστασιολόγηση του με βασικούς υπολογισμούς και την χρήση πεπερασμένων στοιχείων για τον έλεγχο τοπικών υπεφορτίσεων που δεν ήταν εφικτό να προσδιοριστούν με αναλυτικές σχέσεις. Ο θόλος επιρεάζεται από την ταχύτητα των θαλασσίων ρευμάτων που κινούνται γύρω του και αποτελούν τις κύριες δυνάμεις που τον επιρεάζουν. Η μοντελοποίηση της δυναμικής πίεσης πάνω στον αγωγό γίνεται με την χρήση υδροδυναμικού μοντέλου σε FLUENT ενώ η δομική του αντοχή προσδιορίστηκε με χρήση μοντέλου πεπερασμένων στοιχείων σε NASTRAN/ PATRAN. Οι δυνάμεις μεταφέρονταν στα καλώδια ενίσχυσης του θόλου που με την σειρά τους τις μμετέφεραν στο σύστημα αγκύρωσης στον βυθό. Το σύστημα αγκύρωσης διαστασιολογείται με αναλυτικούς υπολογισμούς από την βιβλιογραφία με βάση την μέγιστη δύναμη που μεταφέρεται από τα καλώδια αγκύρωσης του θόλου. Οι διαστάσεις του είναι συνάρτηση τόσο της σύστασης του βυθού όσο και της μέγιστης επιτρεπόμενης διάστασης που επιλέγεται από τα πλοία που συμμετέχουν στην ανάπτυξη του συστήματος. Τα βασικά συμπεράσματα που προέκυψαν από την ανάλυση ήταν η δυνατότητα της περαιτέρω ανάπτυξης του συστήματος σε ρηχά και πολύ βαθιά ύδατα καθώς και η ανάγκη για την μείωση του χρόνου κατασκευής ώστε να αυξηθεί η αποδοτικότητα του συστήματος. / In this PhD work, the mechanical design of a Sub sea Oil Recovery Structure is carried out. The structure is consisted of 6 different parts. The mechanical design methodology starts with the calculation of the diameter of the mooring lines for a tension force of 10000 kN. The fluid/ structure interaction is a design aspect for the Riser tube. Analytical equations were used to identify the dimensions of each riser tube’s part in order to avoid Vortex Induced Vibrations (VIV). As a second step, the oil upward movement into the riser tube was investigated. The buoyancy flow was examined using CFD analysis for both, vertical and inclined tube position to confirm that the crude oil could overcome the frictional forces due to contact with the internal tube’s wall. The external flow field around the riser tube, with the mooring lines along its periphery, was investigated in order to calculate the hydrodynamic coefficients for a range from 0.1 to 0.7 m/sec. This analysis was necessary since it helps to quantify the hydrodynamic load for the structural analysis. The structural analysis for the riser tube parts was performed using FEM and it was used for the study of the behavior under “local” loads such as the sea current’s dynamic pressure. The Buffer Bell’s analysis is based on the prediction of hydrodynamic coefficients (obtained from CFD analysis) and the use of a FE model for the structural analysis of the Buffer Bell hull subject to the hydrostatic pressure. The maximum displacement of the system due to the sea currents was also examined. A scale model test was performed in a water tunnel and a dynamic response model was created in order to predict the system’s behavior under operational loads and during the deployment phase. Additional, a FE model was developed to predict the loads (forces and moments) acting on the stiffening rings and the dome interface unit during the operational scenario. This FE model was compared with the Dynamic Response Model for the maximum displacement criterion. The maximum loads (forces and moments) from the Maximum Displacement FE model was used for the calculation of the dimensions of the stiffening ring and the dome interface unit. Finite element models were developed for these two components. A CFD analysis was performed to investigate the pressure distribution over the surface of the Dome. This pressure load and the reaction forces resulted from the analysis of the Dome Interface Unit were used to calculate the stresses faced by the Dome and the total force applied on the mooring system. For the dimensioning of the anchoring system, the highest force calculated for the mooring lines was chosen. The volume of cement for the anchoring system was calculated in order to withstand this force. Analytical equations were used to secure the anchor’s stability on different types of seabed (cohesion or cohesion less). At the end, the maximum calculated force on the mooring line was compared against the force resulted during the first step in order to confirm that fracture does not occur. The conclusions from this analysis is that the system can be applied to all depths (shallow waters, ultra deep waters) but also the final erection time should be minimized in order to increase the system’s efficiency.

Aviation industry is continuously growing especially for very long distance flights due to the globalisation of local economies around the world and the explosive economic growth in Asia. Reducing the time of intercontinental flights from 16-20 hours to 4 hours or less would therefore make the, already booming, ultra-long distance aviation sector even more attractive. To accomplish this drastic travel time reduction for civil transport, hypersonic cruise aircraft are considered as a potential cost-effective solution. Such vehicles should also be fuelled by liquid hydrogen, which is identified as the only viable propellant to achieve antipodal hypersonic flight with low environmental impact. Despite considerable research on hypersonic aircraft and hydrogen fuel, several major challenges should still be addressed before such airliner becomes reality. The current thesis is therefore motivated by the potential benefit of hydrogen-fuelled hypersonic cruise vehicles associated with their limited state-of-the-art.Hypersonic cruise aircraft require innovative structural configurations and thermal management solutions due to the extremely harsh flight environment, while the uncommon physical properties of liquid hydrogen, combined with high and long-term heat fluxes, introduce complex design and technological storage issues. Achieving hypersonic cruise vehicles is also complicated by the multidisciplinary nature of their design. In the scope of the present research, appropriate methodologies are developed to assess, design and optimize the thermo-structural model and the cryogenic fuel tanks of long-range hydrogen-fuelled hypersonic civil aircraft. Two notional vehicles, cruising at Mach 5 and Mach 8, are then investigated with the implemented methodologies. The design analysis of light yet highly insulated liquid hydrogen tanks for hypersonic cruise vehicles indicates an optimal gravimetric efficiency of 70-75% depending on insulation system, tank wall material, tank diameter, and flight profile. A combination of foam and load-bearing aerogel blanket leads to the lightest cryogenic tank for both the Mach 5 and the Mach 8 aircraft. If the aerogel blanket cannot be strengthened sufficiently so that it can bear the full load, then a combination of foam and fibrous insulation materials gives the best solution for both vehicles. The aero-thermal and structural design analysis of the Mach 5 cruiser shows that the lightest hot-structure is a titanium alloy construction made of honeycomb sandwich panels. This concept leads to a wing-body weight of 143.9 t, of which 36% accounts for the wing, 32% for the fuselage, and 32% for the cryogenic tanks. As expected, hypersonic thermal loads lead to important weight penalties (of more than 35%). The design of the insulated cold structure, however, demonstrates that the long-term high-speed flight of the airliner requires a substantial thermal protection system, such that the best configuration (obtained by load-bearing aerogel blanket) leads to a titanium cold design of only 4% lighter than the hot structure. Using aluminium 7075 rather than titanium offers a further weight saving of about 2%, resulting in a 135.4 t wing-body weight (with a contribution of 23%, 25%, 18% and 34% from the TPS, the wing, the fuselage, and the cryogenic tanks respectively). Given the design hypotheses, the difference in weight is not significant enough to make a decisive choice between hot and cold concepts. This requires the current methodologies to be further elaborated by relaxing the simplifications. Investigation of the thermal protection must be extended from one single point to different regions of the vehicle, and the TPS thickness and weight should be considered in the structural sizing of the cold design. More generally, the design process should be matured by including additional (static, dynamic and transient) loads, special structural concepts, multi-material configurations and other parameters such as cost and safety aspects. / Doctorat en Sciences de l'ingénieur et technologie / This thesis was conducted in co-tutelle between University of Sydney and Université Libre de Bruxelles.Professor Dries Verstraete was my supervisor at the University of Sydney (so as a member of SydneyUni), but is automatically registered here as a member of ULB because he worked at ULB almost ten years ago.Ben Thornber is also a member of the University of Sydney but the application does not save it for an unknown reason. / info:eu-repo/semantics/nonPublished

Submitted to the Department of Electrical Engineering in Fulfilment of the Requirements for the Magister Technologiae in Electrical Engineering at the Cape Peninsula University of Technology SUPERVISOR: E. VOSS NOVEMBER 2013 / The reluctance synchronous machine (RSM) operates on the principle of magnetic reluctance, which is produced through a careful selection of rotor flux barriers and cut-outs. Magnetic reluctivity is the resistance to magnetic flux and can be directly related to the principles of Ohm’s law in electrical circuits. Although reluctance motors have been known for more than 150 years, researchers lost interest when Nikola Tesla’s induction machine (IM) was introduced to industry. Over the last few decades, however, RSMs have shown a lot of potential. They are cheap, robust, reliable, and their rotors can also be used in the stators of IMs. The disadvantage of these machines is an inherently high torque ripple, being the result of its rotor geometry, but the biggest advantage is having a significant reduction in copper losses after the rotor cage has been removed. This advantage drove engineers to investigate, optimise and modify the performance and structure of this machine, which led to the usage of electronic drive systems. The recent advances in technology have allowed researchers to further investigate and modify the design and performance of this special type of machine, with the integration of Finite Element Analysis (FEA) software also making a contribution to the development of the RSM’s current driven systems. The voltage-fed RSM, driven direct-on-line (DOL) from the utility supply, was left in the shadows as the current-fed RSM took reign, but still is, in the author’s opinion, not yet fully analysed. This thesis practically investigates the performance characteristics of the cageless, voltage-fed 3kW RSM in its steady-state operation, under various loads. These performance characteristics are also compared to a RSM driven from a sensorless vector drive (current-fed) to investigate the advantages and disadvantages between the two. Experiments performed on the test bench immediately reveal a limitation to the voltage-fed RSM’s ability to drive higher loads. While the current-fed RSM conveniently reaches 150% of its full-load, the voltage-fed RSM, due to its cageless structure, only reaches 110% of its full-load power. Despite this discovery, the voltage-fed RSM proves to have a lower core loss, harmonic content and torque ripple. Using a FE software package with an integrated source-code, additional parameters such as the dq-axis inductances and currents are also compared and analysed in terms of its reaction to an increase in load. The eddy-current, hysteresis and excess losses are also analysed as well as the harmonic components caused by the geometry of the RSM. For academic purposes, a fair amount of emphasis is placed on the approach to the problem. The preparation for the FE simulation is explained in detail, providing insight into the FE mathematical model as well as parameter acquisition. These parameters include current angle, friction and windage losses, stator resistance, end-winding leakage reactance, core loss and inertia. The results obtained by the FE model are compared to that of the measured results and is found to have an error of only 0.52%. Furthermore, this study attempts to find the feasibility of the voltage-fed RSM’s practicality in modern-day industry. The conclusion is drawn that the voltage-fed RSM could be used as a more elegant alternative to an otherwise over-complicated and over-priced installation.

Nous avons développé un modèle numérique du traitement des anévrismes de l'aorte abdominale (AAA) en utilisant l'analyse par éléments finis (FEA). L'objectif est de simuler les différentes étapes de la procédure endovasculaire dans la phase préopératoire. Pour cela, dans un premier temps, on a fait des études expérimentales Macro et Nano de rupture, indentation, traction, frottement des outils métalliques et des biomatériaux. Ensuite, on a développé une nouvelle approche de la conception des structures anatomiques très angulées et hétérogènes, et enfin, on a crée une maquette numérique de l’interaction outils métalliques et biomatériaux. Dans ce modèle, nous avons pris en compte la géométrie réelle reconstituée à partir des scans, une caractérisation locale des propriétés mécaniques guide / cathéter, une cartographie des propriétés des matériaux composites en fonction de la qualité pariétale, et une projection de l'environnement de l’artère dans l’outil de simulation. Nos résultats ont été validés grâce à un recalage entre les données cliniques et notre simulation pour un groupe donné de patients, dont les artères sont très tortueuses et calcifiées. Cet outil d’aide à l’acte chirurgical permet de contrôler avec précision la navigation endovasculaire en péropératoire, prédire la faisabilité de la chirurgie avec une fiabilité ainsi que d’optimiser le nombre d’outils métalliques pour chaque patient, en tenant compte du risque de rupture des zones avec fortes tortuosités et hétérogénéités. / We have developed a numerical model of the treatment of abdominal aortic aneurysms (AAA) using finite element analysis (FEA) to simulate the endovascular procedure in the preoperative phase. The goal is to simulate different stages of the endovascular procedure. In the model, we took into account the geometry of the biological region reconstructed from scans, a local characterization of the guidewire/catheter mechanical properties, a mapping of material properties depending on the degree of calcification, and a projection of the aorta environment . Our results were validated based on a tuning between clinical data and our simulation for a given group of patients with very tortuous and calcified arteries. It allows to control with accuracy the delivery system rise during surgery, predict the feasibility of the surgery with reliability as well as choose the best guide for each patient, taking into account the risk of rupture of calcified areas in the case of high angulations.

The aim of this thesis is to description and comparison of solutions, demountable connection of the lid and box enclosure air filters for motor vehicles, developed and used by the manufacturing concern MANN + HUMMEL, for which air filtration only one part of a broad portfolio of filtration systems for the automotive industry in the world scale. Another part of this thesis will be one of the chosen optimization methods of connection and implementation of alternative proposals design solutions, including the selection of the best solution, creating design calculation, 3D design, FEA analysis and prototyping of an alternative connection method laser sintering. When creating the optimization and design of alternative design solutions can count on the possibility that existing solutions are taking all possible factors and that the best alternative design proposals show an improvement over existing at the expense of all other cells throughout the development of the product.

The reliability of modern gas turbine engines is largely due to careful damage tolerant design a method of structural design based on the assumption that flaws (cracks) exist in any structure and will continue to grow with usage. With proper monitoring, largely in the form of periodic inspections at conservative intervals reliability and safety is maintained. These methods while reliable can lead to the early retirement of some components and unforeseen failure if design assumptions fail to reflect reality. With improvements to sensor and computing technology there is a growing interest in a system that could continuously monitor the health of structural aircraft as well as forecast future damage accumulation in real-time. Through the use of two-dimensional and three-dimensional numerical modeling the initial goals and findings for this continued work include: (a) establishing measurable parameters directly linked to the health of the blade and (b) the feasibility of detecting accumulated damage to the structural material and thermal barrier coating as well as the onset of damage causing structural failure.

Wood structural elements are more vulnerable to blast loading due to the inherent brittle nature and low density of the material, as demonstrated by recent significant research efforts on the behaviour of timber elements subjected to the effect of blast loading. These studies showed that wood performs poorly under blast loading. A way of improving this performance is to provide additional ductility or energy absorption capabilities to wooden elements. Recently, there was interest in investigating and developing energy-absorbing connections (EAC) to improve timber assemblies’ ductility and energy absorption capabilities. Although some research effort has been made to investigate the use of EACs to enhance the ductility of reinforced concrete or structural steel members, only limited work is available on this topic about timber elements. The current study aims to systematically investigate the use of various shapes of EACs to be used to enhance the post-peak performance of timber assemblies. Preliminary finite element analysis led to selecting nine steel EACs with varying geometries for further experimental investigation. A total of eighteen specimens were tested statically. In comparison, a total of eighteen specimens were tested dynamically in the shock tube facility of the University of Ottawa to simulate the effects of far-field blast explosions. The experimental results showed that decreasing the leg length or increasing the thickness of EACs manufactured with steel angles and reducing the diameter of EACs manufactured with circular HSS caused an increase in yield load and elastic stiffness while reducing the densification displacement. Connections with angles and a centre weld, and connections with 90-degree arcs from circular HSS, were identified as unsuitable for the application of EACs. The experimental program also showed that EACs manufactured from angles offer a well-defined plateau able to absorb a large quantity of energy, making them particularly suitable for blast mitigation. EACs manufactured from multiple circular HSS were shown to achieve multiple load-displacement plateaus and present an interesting option for systems with multiple failure modes occurring at different levels. SDOF analysis and FEA were conducted to predict the experimental behaviour with some success. The importance of the weld type was also highlighted from both the analytical and experimental results. A methodology for developing idealized load-displacement curves from experimental results of EACs was also proposed and evaluated.

Thesis deals with determination of layerwise mechanical properties of composite ceramics by indirect method, namely Youngs modulus. Based on literature review, it was found that a method to determine elastic properties of one or more components of multi layered composites based on experimental modal analysis and finite element modal analysis, or analytical approach exists. Method based on FE modal analysis was applied to ceramic laminate, where it was attempt to determine youngs modulus of one component. Beyond that, it was attempt to determine Youngs moduli of both components using first two bending resonant frequencies. Results were unsatisfying. Sensitivity analysis showed that layers with unknown Youngs modulus were overly sensitive to small changes in input parameters due to their small relative thickness with respect to thickness of laminate and due to location in laminate. Based on this conclusion, recommendations were made with respect to suitable geometry of test specimens.

Diplomová práce se zabývá hodnocením únavové životnosti v okolí konstručního uzlu tlakové nádoby, kde vzniká výrazná koncentrace napětí a je zde předpoklad primárního vlivu na únavu materiálu. Konkrétně se jedná o místo přechodu kontrolního otvoru do pláště analyzovaného zařízení. Práce obsahuje teoretickou a praktickou část. V teoretické části jsou představeny pojmy a metody hodnocení, související s danou problematikou. Na základě těchto metod je provedena analýza konstrukčního uzlu tlakové nádoby. Analýza je provedena metodou konečných prvků na skořepinovém a objemovém modelu nádoby v softwaru ANSYS Workbench, její výsledky dále zpracovány a vyhodnoceny dle aktuálního návrhu úpravy evropské harmonizované normy EN 13445--3, kapitoly 18. Výsledky analýz jsou hodnoceny v závěru práce.

In this thesis is wrote up a complete procedure of stator core stiffness determination using finite element method (FEM), subsequently, the stator core stiffness database was created according to this procedure. In the next chapter is carried out a sensitivity analysis of one chosen stator core, which led to identifying parameters that affected its stiffness the most. Finally, a modal analysis of one synchronous machine was performed using FEM, in order to determine the effect of stator core stiffness on modal characteristics of the machine. Several modal shapes and corresponding natural frequencies were computed in this analysis, then only a few shapes with the highest core effect were chosen and compared.