This document details the design, implementation, testing, and analysis of an inverted short baseline acoustic positioning system. The system presented here is an above-water, air-based prototype for an underwater acoustic positioning system; it is designed to determine the position of remotely-operated underwater vehicles (ROVs) and autonomous underwater vehicles (AUVs) in the global frame using a method that does not drift over time. A ground-truth positioning system is constructed using a stacked hexapod platform actuator, which mimics the motion of an AUV and provides the true position of an ultrasonic microphone array. An ultrasonic transmitter sends a pulse of sound towards the array; microphones on the array record the pulse of sound and use the time shift between the microphone signals to determine the position of the transmitter relative to the receiver array. The orientation of the array, which is necessary to transform the position estimate to the global frame, is calculated using a Madgwick filter and data from a MEMS IMU. Additionally, a dead reckoning change-in-position estimate is formed using the IMU data. The acoustic position estimate is combined with the dead reckoning estimate using a Kalman filter. The accuracy of this filtered position estimate was verified to 22.1mm within a range of 3.88m in this air-based implementation. The ground-truth positioning system runs on an ESP32 microcontroller using code written in C++, and the acoustic positioning system runs on two STM32 microcontrollers using code written in C. Extrapolation of these results to the underwater regime, as well as recommendations for improving upon this work, are included at the end of the document. All code written for this thesis is available on GitHub and is open-source and well-documented.

The development of a numeric simulation for predicting the performance of an Ocean Current Energy Conversion System is presented in this thesis along with a control system development using a PID controller for the achievement of specified rotational velocity set-points. In the beginning, this numeric model is implemented in MATLAB/Simulink® and it is used to predict the performance of a three phase squirrel single-cage type induction motor/generator in two different cases. The first case is a small 3 meter rotor diameter, 20 kW ocean current turbine with fixed pitch blades, and the second case a 20 meter, 720 kW ocean current turbine with variable pitch blades. Furthermore, the second case is also used for the development of a Voltage Source Variable Frequency Drive for the induction motor/generator. Comparison among the Variable Frequency Drive and a simplified model is applied. Finally, the simulation is also used to estimate the average electric power generation from the 720 kW Ocean Current Energy Conversion System which consists of an induction generator and an ocean current turbine connected with a shaft which modeled as a mechanical vibration system.

Monitoring the mechanical integrity of critical structures is extremely important, as mechanical defects can potentially have adverse impacts on their safe operability throughout their service life. Structural defects can be detected by using active structural health monitoring (SHM) approaches, in which a given structure is excited with harmonic mechanical waves generated by actuators. The response of the structure is then collected using sensor(s) and is analyzed for possible defects, with various active SHM approaches available for analyzing the response of a structure to single- or multi-frequency harmonic excitations. In order to identify the appropriate excitation frequency, however, the majority of such methods require a priori knowledge of the characteristics of the defects under consideration. This makes the whole enterprise of detecting structural defects logically circular, as there is usually limited a priori information about the characteristics and the locations of defects that are yet to be detected. Furthermore, the majority of SHM techniques rely on sensors for response collection, with the very same sensors also prone to structural damage. The Surface Response to Excitation (SuRE) method is a broadband frequency method that has high sensitivity to different types of defects, but it requires a baseline. In this study, initially, theoretical justification was provided for the validity of the SuRE method and it was implemented for detection of internal and external defects in pipes. Then, the Comprehensive Heterodyne Effect Based Inspection (CHEBI) method was developed based on the SuRE method to eliminate the need for any baseline. Unlike traditional approaches, the CHEBI method requires no a priori knowledge of defect characteristics for the selection of the excitation frequency. In addition, the proposed heterodyne effect-based approach constitutes the very first sensor-less smart monitoring technique, in which the emergence of mechanical defect(s) triggers an audible alarm in the structure with the defect. Finally, a novel compact phased array (CPA) method was developed for locating defects using only three transducers. The CPA approach provides an image of most probable defected areas in the structure in three steps. The techniques developed in this study were used to detect and/or locate different types of mechanical damages in structures with various geometries.

Die FEM-MKS-Kopplung erfordert Modellordnungsreduktions-Verfahren, die mit kleiner reduzierter Systemdimension das Übertragungsverhalten mechanischer Strukturen abbilden. Rationale Krylov-Unterraum-Verfahren, basierend auf dem Arnoldi-Algorithmen, ermöglichen solche Abbildungen in frei wählbaren, breiten Frequenzbereichen. Ziel ist der Entwurf einer fehlerüberwachten Modelreduktion auf Basis von Krylov-Unterraumverfahren und Anwendung auf ein strukturmechanisches Model. Auf Grundlage der Software MORPACK wird eine Arnoldi-Funktion erster Ordnung um interpolativen Startvektor, Eliminierung der Starrkörperbewegung und Reorthogonalisierung erweitert. Diese Operationen beinhaltend, wird ein rationales, interpolatives SOAR-Verfahren entwickelt. Ein rationales Block-SOAR-Verfahren erweist sich im Vergleich als unterlegen. Es wird interpolative Gleichwichtung verwendet. Das Arnoldi-Verfahren zeichnet kleiner Berechnungsaufwand aus. Das rationale, interpolative SOAR liefert kleinere reduzierte Systemdimensionen für gleichen abgebildeten Frequenzbereich. Die Funktionen werden auf Rahmen-, Getriebegehäuse- und Treibsatzwellen-Modelle angewendet. Zur Fehlerbewertung wird eigenfrequenzbasiert ein H2-Integrationsbereich festgelegt und der übertragungsfunktionsbasierte, relative H2-Fehler berechnet. Es werden zur Lösung linearer Gleichungssysteme mit Matlab entsprechende Löser-Funktionen, auf Permutation und Faktorisierung basierend, implementiert. / FEM-MKS-coupling requires model order reduction methods to simulate the frequency response of mechanical structures using a smaller reduced representation of the original system. Most of the rational Krylov-subspace methods are based on Arnoldi-algorithms. They allow to represent the frequency response in freely selectable, wide frequency ranges. Subject of this thesis is the implementation of an error-controlled model order reduction based on Krylov-subspace methods and the application to a mechanical model. Based on the MORPACK software, a first-order-Arnoldi function is extended by an interpolative start vector, the elimination of rigid body motion and a reorthogonalization. Containing these functions, a rational, interpolative Second Order Arnoldi (SOAR) method is designed that works well compared to a rational Block-SOAR-method. Interpolative equal weighting is used. The first-order-Arnoldi method requires less computational effort compared to the rational, interpolative SOAR that is able to compute a smaller reduction size for same frequency range of interest. The methods are applied to the models of a frame, a gear case and a drive shaft. Error-control is realized by eigenfrequency-based H2-integration-limit and relative H2-error based on the frequency response function. For solving linear systems of equations in Matlab, solver functions based on permutation and factorization are implemented.

Cette thèse étudie des ondes localisées pour certaines classes d'équations différentielles non linéaires décrivant des systèmes mécaniques excitables. Ces systèmes correspondent à une chaîne infinie de blocs reliés par des ressorts et qui glissent sur un surface en présence d'une force de frottement non linéaire dépendant de la vitesse. Nous analysons à la fois le modèle de Burridge-Knopoff (avec des blocs attachés à des ressorts tirés à une vitesse constante) et une chaîne de blocs libres glissant sur un plan incliné sous l'effet de la gravité. Pour une classe de fonctions de frottement non-monotones, ces deux systèmes présentent une réponse de grande amplitude à des perturbations au-dessus d'un certain seuil, ce qui constitue l'une des principales propriétés des systèmes excitables. Cette réponse provoque la propagation d'ondes solitaires ou des fronts, en fonction du modèle et des paramètres. Nous étudions ces ondes localisées numériquement et théoriquement pour une grande gamme de lois de frottement et des régimes de paramètres, ce qui conduit à l'analyse d'équations différentielles non linéaires avec avance et retard. Les phénomènes d'extinction de propagation et d'apparition d'oscillations sont également étudiés pour les ondes progressives. L'introduction d'une fonction de frottement linéaire par morceaux permet de construire explicitement des ondes localisées sous la forme d'intégrales oscillantes et d'analyser certaines de leurs propriétés telles que la forme et la vitesse d'ondes. Une preuve de l'existence d'ondes solitaires est obtenue pour le modèle de Burridge-Knopoff pour un couplage faible. / This thesis analyses localized travelling waves for some classes of nonlinearlattice differential equations describing excitable mechanical systems. Thesesystems correspond to an infinite chain of blocks connected by springs and sliding on a surface in the presence of a nonlinear velocity-dependent friction force. We investigate both the Burridge-Knopoff model (with blocks attached to springs pulled at constant velocity) and a chain of free blocks sliding on an inclined plane under the effect of gravity. For a class of non-monotonic friction functions, both systems display a large response to perturbations above a threshold, one of the main properties of excitable systems. This response induces the propagation of either solitary waves orfronts, depending on the model and parameter regime. We study these localized waves numerically and theoretically for a broad range of friction laws and parameter regimes, which leads to the analysis of nonlinear advance-delay differential equations. Phenomena of propagation failure and oscillations of the travelling wave profile are also investigated. The introduction of a piecewise linear friction function allows one to construct localized waves explicitly in the form of oscillatory integrals and to analyse some of their properties such as shape and wave speed. An existence proof for solitary waves is obtained for the excitable Burridge-Knopoff model in the weak coupling regime.

Réduire l’énergie générée par le frottement et dissipée dans les systèmes mécaniques réels est un des challenges actuels en tribologie. Ce point représente une importance toute particulière dans le domaine des transports terrestres. En réponse à cette nécessité, les constructeurs automobiles se concentrent sur la réduction de la consommation d'énergie en sélectionnant des lubrifiants et des matériaux appropriés d'une part et les systèmes mécaniques performants d'autre part. Grâce à leurs propriétés physiques et tribologiques en termes de réduction de la friction et de l'usure, les couches minces de DLC (Diamond-like Carbon) sont considérées comme l'une des solutions. Le comportement tribologique de couches minces de ta-C (carbone amorphe très dur dépourvu d’hydrogène) et de a-C:H (carbone amorphe hydrogéné) est ici exploré. D’autre part, des “lubrifiants verts“ et des additifs participant aussi à la réduction du frottement et de l'usure sont testés. Ces essais sont effectués dans différentes conditions en utilisant une nouvelle méthodologie expérimentale. Le tribomètre dynamique oscillant développé au LTDS possède la capacité de quantifier avec une très grande précision et sans recourir à une quelconque mesure de force, des niveaux de frottement faibles (dans la gamme 10 – 5 à 10 – 2), et permet en plus d’identifier différentes contributions du frottement. Dans un premier temps, une loi de frottement linéaire a été utilisée afin d’évaluer deux contributions de frottement. La première, μ0 est le coefficient transitoire de frottement quand la vitesse s’annule au changement de direction (du type frottement de Coulomb). La seconde, μ1, est une contribution dépendante de la vitesse de glissement. Ensuite, une étude numérique a été réalisée en appliquant une loi de frottement quadratique afin de mieux comprendre l'aspect dynamique des réponses libres. Cela nous a permis d'étudier numériquement la décroissance d’amplitude des oscillations déterminée grâce à la méthode de moindres carrés. Nous nous intéressons aussi à l‘étude des formes de l'enveloppe de ces oscillations en relation avec le modèle de frottement. Les résultats numériques et expérimentaux pour les lois de frottement linéaire et quadratique sont ensuite comparés. En complément, nous avons mesuré la force tangentielle correspondant aux tribosystèmes testés. Finalement, nous avons étudié numériquement un système dynamique masse-ressort à un degré de liberté, modélisé par la loi de frottement LuGre. Cette loi est décrite par le phénomène d’hystérésis et l’effet de décalage de temps qui ont été détectés expérimentalement. Les résultats expérimentaux obtenus avec le tribomètre oscillant montrent qu'ils sont qualitativement comparables à ceux obtenus en configuration classique cylindre-plan, travaillant à vitesse de glissement constante. Dans tous les cas, les résultats montrent la supériorité du tribosystème ta-C/ta-C dans la réduction du frottement μ0. De plus, les résultats numériques et expérimentaux sont cohérents. Cette étude montre qu’une loi de frottement quadratique est capable de décrire correctement toutes les formes d’enveloppes obtenues expérimentalement : droite, convexe, concave et une combinaison des formes convexe et concave. / Controlling friction is a one of the most significant challenges in the field of tribology. Its major purpose is directed towards the reduction of energy in real mechanical systems, especially in the area of transportation. In response to this necessity, the automobile industries are emphasizing on minimizing the consumption of energy by selecting the appropriate lubricants and materials on one hand and mechanical system with high performance on the other hand. DLC (Diamond-like carbon) coated surfaces are considered one of the solutions thanks to their physical and tribological properties in reducing friction and wear. In this study, we have been interested in investigating the friction behavior of both amorphous hydrogenated (a-C:H) and hydrogen-free tetrahedral amorphous carbon (ta-C) DLC coatings. Furthermore, some “green lubricants” and additives are tested which play a role in reducing friction and wear. These latter tests are performed at different operating conditions using a new experimental methodology, known as the dynamic oscillating tribometer. This original tribometer, developed at the Laboratory of Tribology and System Dynamics (LTDS), is able to measure the oscillatory motion corresponding to various tribosystems having low friction. This technique has the ability to quantify with remarkable precision and without any force transducer, low friction values (in the range of 10 – 5 to 10 – 2 ) and also to evaluate different friction contributions from the displacement and velocity-time responses of a mass-springdamper oscillating system. First, a linear friction law has been used for the systems tested in order to calculate two contributions of friction. The first one, μ0 is the transient friction coefficient at zero speed and the second one (Coulomb-type fiction), μ is a velocitydependent friction coefficient. Then, a numerical study is carried out in order to better understand the dynamic aspect of the oscillatory vibratory free responses. A quadratic friction law is used to model on the mechanical system of the apparatus. This allows us to study numerically the behavior of the decreasing amplitudes of the damping responses which are determined using the Averaging method. Furthermore, we are interested in studying the various forms of these oscillations’ envelop in relation with the polynomial expansion of the friction model. Also, numerical and experimental results are compared using both the linear and quadratic friction models. In addition, a particular attention is given to the measured tangential forces corresponding to our tribosystems. Finally, we study numerically a damped mass-spring single degree-of-freedom mechanical system, induced by LuGre friction law described by both hysteresis and lag effect which have been detected experimentally. Results show that friction tests performed with the oscillating tribometer can be qualitatively compared to those obtained with a conventional tribometer. Moreover, ta-C/ta-C surfaces reveal the lowest friction μ0 when tested by both oscillating and reciprocating tribometers. Also, both numerical and experimental results are found to be of good agreement. This study shows that a quadratic friction law is able to describe correctly the envelopes observed in our experimental tests: straight, convex, concave and a combination of both convex and concave.

MEMS Sensors are widely used for sensing inertial displacements. The displacements arising out of acceleration /Coriolis effect are typically in the range of 1 nm-1 m. This work investigates the realization of high resolution MEMS inertial sensors using novel displacement sensing mechanisms. Capacitance sensing ASIC is developed as part of conventional electronics interface with MEMS sensor under the conventional CMOS-MEMS integration strategy. The capacitance sense ASIC based on Continuous Time Voltage scheme with coherent and non-coherent demodulation is prototyped on AMS 0.35 m technology. The ASIC was tested to sense C = 3.125 fF over a base of 2 pF using on-chip built-in test capacitors. Dynamic performance of this ASIC was validated by interfacing with a DaCM MEMS accelerometer. 200milli-g of acceleration (equivalent to a C = 2.8 fF) over an input frequency of 20Hz is measurable using the developed ASIC. The observed sensitivity is 90mV/g. The ASIC has several programmable features such as variation in trim capacitance (3.125 fF-12.5 pF), bandwidth selection (500 Hz-20 kHz) and variable gain options (2-100). Capacitance detection, a dominant sensing principle in MEMs sensors, experiences inherent limitation due to the role of parasitics when the displacements of interest are below 5 nm range. The capacitive equivalence ( C) for the range of displacements of the order of 5 nm and below would vary in the range atto-to-zepto farad. Hence there is a need to explore alternative sensing schemes which preferably yield higher sensitivity (than those offered by the conventional integration schemes) and are based on the principle of built-in transduction to help overcome the influence of parasitics on sensitivity. In this regard, 3 non-conventional architectures are explored which fall under the direct integration classification namely: (a) Sub-threshold based sensing (b) Fringe field based sensing and (c) Tunneling current based sensing. a) In Sub-threshold based sensing, FET with a suspended gate is used for displacement sensing. The FET is biased in the sub-threshold region of operation. The exponential modulation of drain current for a change in displacement of 1 nm is evaluated using TCAD, and the in uence of initial air-gap variation on the sensitivity factor ( ID=ID) is brought out. For 1% change in air gap displacement (i.e., TGap/TGap, the gap variation resulting due to the inertial force / mass loading) nearly 1050% change in drain current( ID=ID) is observed (considering initial air gaps of the order 100 nm). This validates the high sensitivity offered by the device in this regime of operation. A comparison of sensitivity estimate using the capacitive equivalence model and TCAD simulated model for different initial air-gaps in a FD-SOI FET is brought out. The influence of FDSOI FET device parameters on sensitivity, namely the variation of TSi, TBox, NA and TGap are explored. CMOS compatibility and fabrication feasibility of this architecture was looked into by resorting to the post processing approach used for validating the sub-threshold bias concept. The IMD layers of the Bulk FETs fabricated through AMS 0.35 technology were etched using BHF and IPA mixture to result in a free standing metal (Al) layers acting as the suspended gate. The performance estimate is carried out considering specific Equivalent Gap Thickness (EGT) of 573 nm and 235 nm, to help overcome the role of coupled electrostatics in influencing the sensitivity metric. The sensitivity observed by biasing this post processed bulk FET in sub-threshold is 114% ( ID=ID change) for a 59% ( d/d change). The equivalent C in this case is 370 aF. b) In Fringe eld based sensing approach, a JunctionLess FET (JLFET) is used as a depletion mode device and an out-of-plane gate displacement would help modulate the device pinch-o voltage due to fringe field coupling. The resulting change in the gate fringe field due to this displacement modulates the drain current of the JunctionLess FET. The displacement induced fringe field change (relative to the FET channel) brings about a distinct shift in the ID-VG characteristics of the JLFET. For displacement d = 2 nm, the JLFET with a channel doping of ND = 8X1018cm 3 and a bias point of VG = -47.7 V, 98% enhancement in sensitivity is observed in 3D TCAD simulations. The equivalent C in this case is 29 zF. The role of ground-planes in the device operation is explored. c) In the tunneling current based sensing approach, the beams fabricated using the SOI-MUMPS process are FIB milled so as to create very ne air gaps of the order of nearly 85 nm. Under high electric fields of the order > 8 MV/cm, the lateral displacement based tunneling sensor offers enhanced change in sensitivity for an induced external force at a fixed DC bias. When integrated as an array with varying electrode overlap, this technique can track displacements over a wide range. With the initial beam overlap as 1.2 m, for a lateral displacement of 1.2 m, a 100% change in sensitivity ( ID=ID) is observed. The effect of fringe field can be completely neglected here unlike its capacitive beam equivalent.

Cette thèse traite le problème d'intégration hardware optimale de contrôleurs linéaires à taille de mot finie, dédiés aux applications MEMS. Le plus grand défi est d'assurer des performances de contrôle satisfaisantes avec un minimum de ressources logiques. Afin d'y parvenir, deux optimisations distinctes mais complémentaires peuvent être entreprises: en théorie de contrôle et en arithmétique binaire. Seule cette dernière est considérée dans ce travail.Comme cette arithmétique cible des applications MEMS, elle doit faire preuve de vitesse afin de prendre en charge la dynamique rapide des MEMS, à faible consommation de puissance pour un contrôle intégré, hautement re-configurabe pour un ajustement facile des performances de contrôle, et facilement prédictible pour fournir une idée précise sur les ressources logiques nécessaires avant l'implémentation même.L'exploration d'un certain nombre d'arithmétiques binaires a montré que l'arithmétique radix-2r est celle qui répond au mieux aux exigences précitées. Elle a été pleinement exploitée afin de concevoir des circuits de multiplication efficaces, qui sont au fait, le véritable moteur des systèmes linéaires.L'arithmétique radix-2r a été appliquée à l'intégration hardware de deux structures linéaires à taille de mot finie: un contrôleur PID variant dans le temps et à un contrôleur LQG invariant dans le temps,avec un filtre de Kalman. Le contrôleur PID a montré une nette supériorité sur ses homologues existants. Quant au contrôleur LQG, une réduction très importante des ressources logiques a été obtenue par rapport à sa forme initiale non optimisée / This thesis addresses the problem of optimal hardware-realization of finite-word-length(FWL) linear controllers dedicated to MEMS applications. The biggest challenge is to ensuresatisfactory control performances with a minimal hardware. To come up, two distinct butcomplementary optimizations can be undertaken: in control theory and in binary arithmetic. Only thelatter is involved in this work.Because MEMS applications are targeted, the binary arithmetic must be fast enough to cope withthe rapid dynamic of MEMS; power-efficient for an embedded control; highly scalable for an easyadjustment of the control performances; and easily predictable to provide a precise idea on therequired logic resources before the implementation.The exploration of a number of binary arithmetics showed that radix-2r is the best candidate that fitsthe aforementioned requirements. It has been fully exploited to designing efficient multiplier cores,which are the real engine of the linear systems.The radix-2r arithmetic was applied to the hardware integration of two FWL structures: a linear timevariant PID controller and a linear time invariant LQG controller with a Kalman filter. Both controllersshowed a clear superiority over their existing counterparts, or in comparison to their initial forms.

Die FEM-MKS-Kopplung erfordert Modellordnungsreduktions-Verfahren, die mit kleiner reduzierter Systemdimension das Übertragungsverhalten mechanischer Strukturen abbilden. Rationale Krylov-Unterraum-Verfahren, basierend auf dem Arnoldi-Algorithmen, ermöglichen solche Abbildungen in frei wählbaren, breiten Frequenzbereichen. Ziel ist der Entwurf einer fehlerüberwachten Modelreduktion auf Basis von Krylov-Unterraumverfahren und Anwendung auf ein strukturmechanisches Model. Auf Grundlage der Software MORPACK wird eine Arnoldi-Funktion erster Ordnung um interpolativen Startvektor, Eliminierung der Starrkörperbewegung und Reorthogonalisierung erweitert. Diese Operationen beinhaltend, wird ein rationales, interpolatives SOAR-Verfahren entwickelt. Ein rationales Block-SOAR-Verfahren erweist sich im Vergleich als unterlegen. Es wird interpolative Gleichwichtung verwendet. Das Arnoldi-Verfahren zeichnet kleiner Berechnungsaufwand aus. Das rationale, interpolative SOAR liefert kleinere reduzierte Systemdimensionen für gleichen abgebildeten Frequenzbereich. Die Funktionen werden auf Rahmen-, Getriebegehäuse- und Treibsatzwellen-Modelle angewendet. Zur Fehlerbewertung wird eigenfrequenzbasiert ein H2-Integrationsbereich festgelegt und der übertragungsfunktionsbasierte, relative H2-Fehler berechnet. Es werden zur Lösung linearer Gleichungssysteme mit Matlab entsprechende Löser-Funktionen, auf Permutation und Faktorisierung basierend, implementiert.:1. Einleitung 1.1. Motivation 1.2. Einordnung 1.3. Aufbau der Arbeit 2. Theorie 2.1. Simulationsmethoden 2.1.1. Finite Elemente Methode 2.1.2. Mehrkörpersimulation 2.1.3. Kopplung der Simulationsmethoden 2.2. Zustandsraumdarstellung und Reduktion 2.3. Krylov Unterraum Methoden 2.4. Arnoldi-Algorithmen erster Ordnung 2.5. Arnoldi-Algorithmen zweiter Ordnung 2.6. Korrelationskriterien 2.6.1. Eigenfrequenzbezogene Kriterien 2.6.2. Eigenvektorbezogene Kriterien 2.6.3. Übertragungsfunktionsbezogene Kriterien 2.6.4. Fehlerbewertung 2.6.5. Anwendung auf Systeme sehr großer Dimension 3. Numerik linearer Gleichungssysteme 3.1. Grundlagen 3.2. Singularität der Koeffizientenmatrix 3.2.1. Randbedingungen des Systems 3.2.2. Verwendung einer generellen Diagonalperturbation 3.3. Iterative Lösungsverfahren 3.4. Faktorisierungsverfahren 3.4.1. Cholesky-Faktorisierung 3.4.2. LU-Faktorisierung 3.4.3. Fillin-Reduktion durch Permutation 3.4.4. Fazit 3.5. Direkte Lösungsverfahren 3.6. Verwendung externer Gleichungssystem-Löser 3.7. Zusammenfassung 4. Implementierung 4.1. Aufbau von MORPACK 4.2. Anforderungen an Reduktions-Funktionen 4.3. Eigenschaften und Optionen der KSM-Funktionen 4.3.1. Arnoldi-Funktion erster Ordnung 4.3.2. Rationale SOAR-Funktionen 4.4. Korrelationskriterien 4.4.1. Eigenfrequenzbezogen 4.4.2. Eigenvektorbezogen 4.4.3. Übertragungsfunktionsbezogen 4.5. Lösungsfunktionen linearer Gleichungssysteme 4.5.1. Anforderungen und Aufbau 4.5.2. Verwendung der Gleichungssystem-Löser 4.5.3. Hinweise zur Implementierung von Gleichungssystem-Lösern 5. Anwendung 5.1. Versuchsmodelle 5.1.1. Testmodelle kleiner Dimension 5.1.2. Getriebegehäuse 5.1.3. Treibsatzwelle 5.2. Validierung der Reduktionsmethoden an kleinem Modell 5.2.1. Modifizierte Arnoldi-Funktion erster Ordnung 5.2.2. Rationale SOAR-Funktionen 5.2.3. Zusammenfassung 5.3. Anwendung der KSM auf große Modelle 5.3.1. Getriebegehäuse 5.3.2. Treibsatzwelle 5.4. Auswertung 6. Zusammenfassung und Ausblick 6.1. Zusammenfassung 6.2. Ausblick / FEM-MKS-coupling requires model order reduction methods to simulate the frequency response of mechanical structures using a smaller reduced representation of the original system. Most of the rational Krylov-subspace methods are based on Arnoldi-algorithms. They allow to represent the frequency response in freely selectable, wide frequency ranges. Subject of this thesis is the implementation of an error-controlled model order reduction based on Krylov-subspace methods and the application to a mechanical model. Based on the MORPACK software, a first-order-Arnoldi function is extended by an interpolative start vector, the elimination of rigid body motion and a reorthogonalization. Containing these functions, a rational, interpolative Second Order Arnoldi (SOAR) method is designed that works well compared to a rational Block-SOAR-method. Interpolative equal weighting is used. The first-order-Arnoldi method requires less computational effort compared to the rational, interpolative SOAR that is able to compute a smaller reduction size for same frequency range of interest. The methods are applied to the models of a frame, a gear case and a drive shaft. Error-control is realized by eigenfrequency-based H2-integration-limit and relative H2-error based on the frequency response function. For solving linear systems of equations in Matlab, solver functions based on permutation and factorization are implemented.:1. Einleitung 1.1. Motivation 1.2. Einordnung 1.3. Aufbau der Arbeit 2. Theorie 2.1. Simulationsmethoden 2.1.1. Finite Elemente Methode 2.1.2. Mehrkörpersimulation 2.1.3. Kopplung der Simulationsmethoden 2.2. Zustandsraumdarstellung und Reduktion 2.3. Krylov Unterraum Methoden 2.4. Arnoldi-Algorithmen erster Ordnung 2.5. Arnoldi-Algorithmen zweiter Ordnung 2.6. Korrelationskriterien 2.6.1. Eigenfrequenzbezogene Kriterien 2.6.2. Eigenvektorbezogene Kriterien 2.6.3. Übertragungsfunktionsbezogene Kriterien 2.6.4. Fehlerbewertung 2.6.5. Anwendung auf Systeme sehr großer Dimension 3. Numerik linearer Gleichungssysteme 3.1. Grundlagen 3.2. Singularität der Koeffizientenmatrix 3.2.1. Randbedingungen des Systems 3.2.2. Verwendung einer generellen Diagonalperturbation 3.3. Iterative Lösungsverfahren 3.4. Faktorisierungsverfahren 3.4.1. Cholesky-Faktorisierung 3.4.2. LU-Faktorisierung 3.4.3. Fillin-Reduktion durch Permutation 3.4.4. Fazit 3.5. Direkte Lösungsverfahren 3.6. Verwendung externer Gleichungssystem-Löser 3.7. Zusammenfassung 4. Implementierung 4.1. Aufbau von MORPACK 4.2. Anforderungen an Reduktions-Funktionen 4.3. Eigenschaften und Optionen der KSM-Funktionen 4.3.1. Arnoldi-Funktion erster Ordnung 4.3.2. Rationale SOAR-Funktionen 4.4. Korrelationskriterien 4.4.1. Eigenfrequenzbezogen 4.4.2. Eigenvektorbezogen 4.4.3. Übertragungsfunktionsbezogen 4.5. Lösungsfunktionen linearer Gleichungssysteme 4.5.1. Anforderungen und Aufbau 4.5.2. Verwendung der Gleichungssystem-Löser 4.5.3. Hinweise zur Implementierung von Gleichungssystem-Lösern 5. Anwendung 5.1. Versuchsmodelle 5.1.1. Testmodelle kleiner Dimension 5.1.2. Getriebegehäuse 5.1.3. Treibsatzwelle 5.2. Validierung der Reduktionsmethoden an kleinem Modell 5.2.1. Modifizierte Arnoldi-Funktion erster Ordnung 5.2.2. Rationale SOAR-Funktionen 5.2.3. Zusammenfassung 5.3. Anwendung der KSM auf große Modelle 5.3.1. Getriebegehäuse 5.3.2. Treibsatzwelle 5.4. Auswertung 6. Zusammenfassung und Ausblick 6.1. Zusammenfassung 6.2. Ausblick

Les systèmes et matériaux mécaniques non linéaires sont largement utilisés dans divers domaines. Cependant, leur modélisation et leur conception ne sont pas triviales car elles nécessitent une compréhension complète de leurs non-linéarités internes et d'autres phénomènes. Pour permettre une conception efficace, nous devons d'abord introduire des modèles de calcul afin de caractériser avec précision leur comportement complexe. En outre, de nouvelles techniques de conception inverse sont également nécessaires pour comprendre comment le comportement change lorsque nous modifions les paramètres de conception des systèmes mécaniques non linéaires et des matériaux. Par conséquent, dans cette thèse, nous présentons trois nouvelles méthodes pour la modélisation informatique et la conception de systèmes mécaniques non linéaires et de matériaux. Dans le premier article, nous abordons le problème de la conception de systèmes mécaniques non linéaires présentant des mouvements périodiques stables en réponse à une force périodique. Nous présentons une méthode de calcul qui utilise une approche du domaine fréquentiel pour la simulation dynamique et la puissante analyse de sensibilité pour l'optimisation de la conception afin de concevoir des systèmes mécaniques conformes avec des oscillations de grande amplitude. Notre méthode est polyvalente et peut être appliquée à divers types de systèmes mécaniques souples. Nous validons son efficacité en fabriquant et en évaluant plusieurs prototypes physiques. Ensuite, nous nous concentrons sur la modélisation informatique et la caractérisation mécanique des matériaux non linéaires dominés par le contact, en particulier les matériaux à emboîtement discret (DIM), qui sont des tissus de cotte de mailles généralisés constitués d'éléments d'emboîtement quasi-rigides. Contrairement aux matériaux élastiques conventionnels pour lesquels la déformation et la force de rappel sont directement couplées, la mécanique des DIM est régie par des contacts entre des éléments individuels qui donnent lieu à des contraintes de déformation cinématique anisotrope. Pour reproduire le comportement biphasique du DIM sans simuler des structures à micro-échelle coûteuses, nous introduisons une méthode efficace de limitation de la déformation anisotrope basée sur la programmation conique du second ordre (SOCP). En outre, pour caractériser de manière exhaustive la forte anisotropie, le couplage complexe et d'autres phénomènes non linéaires du DIM, nous introduisons une nouvelle approche d'homogénéisation pour distiller des limites de déformation à grande échelle à partir de simulations à micro-échelle et nous développons un modèle macromécanique basé sur des données pour simuler le DIM avec des contraintes de déformation homogénéisées. / Nonlinear mechanical systems and materials are broadly used in diverse fields. However, their modeling and design are nontrivial as they require a complete understanding of their internal nonlinearities and other phenomena. To enable their efficient design, we must first introduce computational models to accurately characterize their complex behavior. Furthermore, new inverse design techniques are also required to capture how the behavior changes when we change the design parameters of nonlinear mechanical systems and materials. Therefore, in this thesis, we introduce three novel methods for computational modeling and design of nonlinear mechanical systems and materials. In the first article, we address the design problem of nonlinear mechanical systems exhibiting stable periodic motions in response to a periodic force. We present a computational method that utilizes a frequency-domain approach for dynamical simulation and the powerful sensitivity analysis for design optimization to design compliant mechanical systems with large-amplitude oscillations. Our method is versatile and can be applied to various types of compliant mechanical systems. We validate its effectiveness by fabricating and evaluating several physical prototypes. Next, we focus on the computation modeling and mechanical characterization of contact-dominated nonlinear materials, particularly Discrete Interlocking Materials (DIM), which are generalized chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring forces are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic kinematic deformation constraints. To replicate the biphasic behavior of DIM without simulating expensive microscale structures, we introduce an efficient anisotropic strain-limiting method based on second-order cone programming (SOCP). Additionally, to comprehensively characterize strong anisotropy, complex coupling, and other nonlinear phenomena of DIM, we introduce a novel homogenization approach for distilling macroscale deformation limits from microscale simulations and develop a data-driven macromechanical model for simulating DIM with homogenized deformation constraints.