Die vorliegende Arbeit befasst sich mit der Methode der modalen Superposition als Ordnungsreduktionsverfahren in der Mikrosystemtechnik. Typische Anwendungsgebiete sind Inertialsensoren und dabei im Besonderen Drehratensensoren, für die die Simulation von zeitabhängigen Phänomenen von entscheidender Bedeutung ist. Im Rahmen der Weiterentwicklung der Ordnungsreduktion nach der Methode der modalen Superposition ist es gelungen für typische lineare Kräfte eine auf analytischen Gleichungen basierende Beschreibung im reduzierten Raum zu finden. Für die Beschreibung von nichtlinearen Kräften ist im Rahmen dieser Arbeit ein Verfahren entwickelt worden, das es erlaubt, bestehende Modelle im Finite-Elemente-Raum in der modalen Beschreibung zu nutzen. In dieser Arbeit werden die theoretischen Grundlagen zur Berücksichtigung von Einflüssen der Aufbau- und Verbindungstechnik in ordnungsreduzierten Modellen dargestellt. Neben der Einkopplung äußerer Kräfte und der Veränderung der mechanischen Randbedingungen wird auch der Einfluss der Aufbau- und Verbindungstechnik auf die elektrostatischen Eigenschaften untersucht. Die Parametrisierung des Verfahrens der modalen Superposition über Fit- und Interpolationsverfahren erlaubt es, parametrisierte ordnungsreduzierte Modelle für die zeitabhängige Systemsimulation zu generieren. Damit wird die Durchführung von Designoptimierung und die Berücksichtigung von Fertigungs- und Prozessschwankungen in ordnungsreduzierten Modellen auf Systemebene möglich.

Being able to accurately approximate outputs of computationally expensive simulations for arbitrary input parameters, also called missing points estimation, is central in many different areas of research and development with applications ranging from uncertainty propagation to control system design to name a few. This project investigates the potential of kernel transformations and nonlinear autoencoders as methods of improving the accuracy of the proper orthogonal decomposition method combined with regression. The techniques are applied on aerodynamic pressure CFD data around airplane wings in both two- and three-dimensional settings. The novel methods show potential in select situations, but cannot at this stage be generally considered superior. Their performances are similar although the procedure of design and training of a nonlinear autoencoder is less straight forward and more time demanding than using kernel transformations. The results demonstrate the regression bottleneck of the proper orthogonal decomposition method, which partially is improved with the new methods. Future studies should focus on adapting the autoencoder training strategy to the architecture and data as well as improving the regression stage of all methods.

Le but de ce travail est d'introduire un cadre d'approximation, la Reference Points Method, afin de réduire la complexité de calcul des opérations algébriques lorsqu'elles concernent des approximations à variables séparées dans le cadre de la Proper Generalized Decomposition.La PGD a été introduite dans [1] dans le cadre de la méthode LaTIn pour résoudre efficacement des équations différentielles non linéaires et dépendants du temps en mécanique des structures. La technique consiste à chercher la solution d'un problème dans une base d'ordre réduit (ROB) qui est automatiquement et à la volée générée par la méthode LaTIn. La méthode LaTIn est une stratégie itérative qui génère les approximations de la solution sur l'ensemble du domaine espace-temps-paramètres par enrichissements successifs. Lors d'une itération particulière, la ROB, qui a déjà été formée, est d'abord utilisée pour calculer un nouveau modèle réduit (ROM) et, donc, pour trouver une nouvelle approximation de la solution. Si la qualité de cette approximation ne suffit pas, la ROB est enrichie avec la génération d'un nouveau produit de fonctions PGD en utilisant un algorithme de type 'greedy'.Les techniques de réduction de modèle sont particulièrement efficaces lorsque le ROM a besoin d'être construit qu'une seule fois. Ce n'est pas le cas pour les techniques de réduction de modèle quand elles concernent des problèmes non linéaires. En effet, dans un tel cas, les opérateurs qui sont impliqués dans la construction du ROM varient au cours du processus itératif et des calculs préliminaires ne peuvent pas être effectués à l'avance pour accélérer le processus 'online'.Par conséquent, la construction du ROM est un élément coûteux de la stratégie de calcul en terme de temps de calcul. Il en découle la nécessité d'évaluer, à chaque itération, la fonction non linéaire de grande dimension (et éventuellement sa jacobienne) et ensuite sa projection pour obtenir les opérateurs réduits. Cela représente un point de blocage des stratégies de réduction de modèle dans le cadre non linéaire. Le présent travail a comme but une réduction ultérieure du coût de calcul, grâce à l'introduction d'un nouveau cadre de rapprochement dédiée à la stratégie de calcul LaTIn-PGD. Il est basé sur la notion de temps, de points et de paramètres de référence et permet de définir une version compressée des données. Comparé à d'autres techniques similaires [3,4] cela ne se veut pas une technique d'interpolation, mais un cadre algébrique qui permet de donner une première approximation, peu coûteuse, de toutes les quantités sous une forme à variable séparés par des formules explicites. L'espace de données compressées présente des propriétés intéressantes qui traitent les opérations algébriques élémentaires. Le RPM est introduit dans le solveur LaTIn-PGD non linéaire pour calculer certaines opérations répétitives. Ces opérations sont liées à la résolution du problème du temps / paramètre qui implique la mise à jour de l'opérateur tangent et la projection de ce dernier sur la base réduite. La RPM permet de simplifier et de réduire le nombre d'opérations nécessaires.[1] Ladevèze P., Sur une famille d’algorithmes en mécanique des structures, Comptes Rendus Académie des Sciences. Paris. Ser. II 300, pp.41-44, 1985.[2] Chinesta, F., Ladevèze, P., and Cueto, E. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering, 18, pp.395-404, 2011.[3] Barrault M., Maday Y., Nguyen N., Patera A., An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Académie des Sciences. Paris. Ser. I, 339, pp. 667-672, 2004.[4] Chaturentabut S., Sorensen D., Nonlinear model reduction via discrete empirical interpolation, Society for Industrial and Applied Mathematics 32(5), pp.2737-2764, 2010. / The aim of this work is to introduce an approximation framework, called Reference Points Method (RPM), in order to decrease the computational complexity of algebraic operations when dealing with separated variable approximations in the Proper Generalized Decomposition (PGD) framework.The PGD has been introduced in [1] in the context of the LATIN method to solve efficiently time dependent and/or parametrized nonlinear partial differential equations in structural mechanics (see, e.g., the review [2] for recent applications). Roughly, the PGD technique consists in seeking the solution of a problem in a relevant Reduced-Order Basis (ROB) which is generated automatically and on-the-fly by the LATIN method. This latter is an iterative strategy which generates the approximations of the solution over the entire time- space-parameter domain by successive enrichments. At a particular iteration, the ROB, which has been already formed, is at first used to compute a projected Reduced-Order Model (ROM) and find a new approximation of the solution. If the quality of this approximation is not sufficient, the ROB is enriched by determining a new functional product using a greedy algorithm.However, model reduction techniques are particularly efficient when the ROM needs one construction only. This is not the case for the model reduction techniques when they are addressed to nonlinear problems. Indeed, in such a case, the operators which are involved in the construction of the ROM change all along the iterative process and no preliminary computations can be performed in advance to speed up the online process. Hence, the construction of the ROM is an expensive part of the calculation strategy in terms of CPU. It ensues from the need to evaluate the high-dimensional nonlinear function (and eventually its Jacobian) and then to project it to get the low-dimensional operators at each computational step of a solution algorithm. This amounts to being the bottleneck of nonlinear model reduction strategies.The present work is then focused on a further reduction of the computational cost, thanks to the introduction of a new approximation framework dedicated to PGD-based nonlinear solver. It is based on the concept of reference times, points and parameters and allows to define a compressed version of the data. Compared to other similar techniques [3,4] this is not an interpolation technique but an algebraic framework allowing to give an inexpensive first approximation of all quantities in a separated variable form by explicit formulas. The space of compressed data shows interesting properties dealing the elementary algebraic operations. The RPM is introduced in the PGD-based nonlinear solver to compute some repetitive operations. These operations are related to the resolution of the time/parameter problem that involves the update of the tangent operator (for nonlinear problems) and the projection of this latter on the Reduced Order Basis. For that the RPM allows to simplify and reduce the number of operations needed.[1] Ladevèze P., Sur une famille d’algorithmes en mécanique des structures, Comptes Rendus Académie des Sciences. Paris. Ser. II 300, pp.41-44, 1985.[2] Chinesta, F., Ladevèze, P., and Cueto, E. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering, 18, pp.395-404, 2011.[3] Barrault M., Maday Y., Nguyen N., Patera A., An ’empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Académie des Sciences. Paris. Ser. I, 339, pp. 667-672, 2004.[4] Chaturentabut S., Sorensen D., Nonlinear model reduction via discrete empirical interpolation, Society for Industrial and Applied Mathematics 32(5), pp.2737-2764, 2010.

No description available.

This thesis describes a novel new method, termed the Tangent-Line-Chord (TLC) method, that can be used to more efficiently model creep deformation dominated by the tertiary regime. Creep deformation is a widespread mechanical mode of failure found in high-stress and temperature mechanical systems. To accurately simulate creep and its effect on structures, researchers utilize finite element analysis (FEA). General purpose FEA packages require extensive amounts of time and computer resources to simulate creep softening in components because of the large deformation rates that continuously evolve. The goal of this research is to employ multi-regime creep models, such as the Kachanov-Rabotnov model, to determine a set of equations that will allow creep to be simulated using as few iterations as possible. The key outcome is the freeing up of computational resources and the saving of time. Because both the number of equations and the value of material constants within the model change depending on the approach used, programming software will be utilized to automate this analytical process. The materials being considered in this research are mainly generic Ni-based superalloys, as they exhibit creep responses that are dominated by secondary and tertiary creep.

<p>Positive displacement machines (PDMs) operate based on the principle of positive displacement, which necessitates a periodic alteration of volume. This volume variation is accomplished through relative motion between machine components. PDMs find extensive applications in diverse domains, encompassing fluid power systems, lubrication systems, fluid transport systems, fuel injection systems, and more. The primary distinction among PDMs lies in the geometric mechanisms employed for fluid displacement, as well as the flow distribution mechanisms they employ. PDMs can be broadly classified into piston machines, vane machines, screw machines, and gear machines. In fluid power systems, the most commonly used PDMs are the piston and gear machines. Piston machines can be further classified into radial piston machines, in-line piston machines, and axial piston machines. The most commonly used piston machines are the axial piston machine owing to their superior efficiency and compactness. Gear machines can be further classified into external gear machines, internal gear machines, and annular gear machines. The most commonly used gear machine is the external gear machine owing to its price.</p> <p><br></p> <p>PDMs typically involve multiple solid bodies in relative motion, with micron-level gaps between them. These gaps, known as lubricating interfaces, present a significant design challenge during the machine development process. They are a primary source of power losses and play a crucial role in determining the efficiency and durability of the machine. The lubricating interfaces must effectively balance loads and maintain a high-pressure fluid seal. Achieving this delicate balance necessitates a comprehensive understanding of the underlying physical phenomena. Lubricating interfaces generate substantial heat due to viscous dissipation, which directly impacts the operation of the entire machine. The viscosity of the working fluid rapidly decays with temperature, causing the warmer fluid within the lubricating interface to possess lower viscosity. Consequently, it can support lesser loads and is more prone to leakage. Moreover, as the solid bodies enclosing the warmer fluid heat up, they undergo thermal expansion, further changing the clearance and leading to a decline in performance. Additionally, the elevated temperature of the fluid within the lubricating interface affects the compressibility of the displacement chamber fluid, thereby influencing the pressurization characteristics of the entire unit. Thus, thermal effects play a critical role in the performance of PDMs.</p> <p><br></p> <p>  The ever-increasing market demand for more compact, efficient, and reliable designs requires a continuous process of design improvements over previous designs, and sometimes completely new designs. Sophisticated simulation tools are a necessity for such a design process. Additionally, these simulation tools also prove to be valuable in formulating design modifications in case of underperforming designs. Due to the complexity associated with the operation of such units, the simulation tools need to capture a wide variety of physical phenomena. Over the past few decades, owing to the increasing computing power of the desktop computer, several simulation tools have been proposed across the literature to aid the design process of such machines with each having limitations of their own.</p> <p><br></p> <p>  The objective of the present thesis is to propose a modeling approach that assists in the design process of positive displacement machines, addressing various limitations identified in the existing literature. The approach is intentionally designed to be generic, enabling its application across a diverse range of positive displacement machines. The modeling approach encompasses three distinct domains: the displacement chamber fluid domain, the lubricating interface fluid domain, and the solid domain. A novel thermal model that integrates all three domains is introduced. </p> <p><br></p> <p>  To validate the effectiveness of the proposed modeling approach, two separate validation studies are conducted. The first study focuses on a model for an isolated piston/cylinder interface of an axial piston machine, operating under the mixed lubrication regime. The model demonstrates a strong agreement with the measured data. The second study involves steady-state measurements of an entire axial piston machine. The model is validated by comparing the steady-state flow characteristics and temperature distribution on the valveplate, both of which are accurately captured by a single fully coupled model. The modeling approach developed in this study, specifically, the energy conservation in the lubricating interface, heat transfer in the solid bodies, and thermal deformation in the solid bodies are all generalized for applicability in different types of PDMs. However, the results presented in this thesis pertain to an axial piston machine.</p>

<div>Adsorbent technology is widely used in many industrial applications including waste heat recovery, water purification, and atmospheric revitalization in confined habitations. Astronauts depend on adsorbent-based systems to remove metabolic carbon dioxide (CO₂) from the cabin atmosphere; as NASA prepares for the journey to Mars, engineers are redesigning the adsorbent-based system for reduced weight and optimal efficiency. These efforts hinge upon the development of accurate, predictive models, as simulations are increasingly relied upon to save cost and time over the traditional design-build-test approach. Engineers rely on simplified models to reduce computational cost and enable parametric optimizations. Amongst these simplified models is the axially dispersed plug-flow model for predicting the adsorbate concentration during flow through an adsorbent bed. This model is ubiquitously used in designing fixed-bed adsorption systems. The current work aims to improve the accuracy of the axially dispersed plug-flow model because of its wide-spread use. This dissertation identifies the critical model inputs that drive the overall uncertainty in important output quantities then systematically improves the measurement and prediction of these input parameters. Limitations of the axially dispersed plug-flow model are also discussed, and recommendations made for identifying failure of the plug-flow assumption.</div><div><br></div><div>An uncertainty and sensitivity analysis of an axially disperse plug-flow model is first presented. Upper and lower uncertainty bounds for each of the model inputs are found by comparing empirical correlations against experimental data from the literature. Model uncertainty is then investigated by independently varying each model input between its individual upper and lower uncertainty bounds then observing the relative change in predicted effluent concentration and temperature (<i>e.g.</i>, breakthrough time, bed capacity, and effluent temperature). This analysis showed that the LDF mass transfer coefficient is the largest source of uncertainty. Furthermore, the uncertainty analysis reveals that ignoring the effect of wall-channeling on apparent axial dispersion can cause significant error in the predicted breakthrough times of small-diameter beds.</div><div><br></div><div>In addition to LDF mass transfer coefficient and axial-dispersion, equilibrium isotherms are known to be strong lever arms and a potentially dominant source of model error. As such, detailed analysis of the equilibrium adsorption isotherms for zeolite 13X was conducted to improve the fidelity of CO₂ and H₂O on equilibrium isotherms compared to extant data. These two adsorbent/adsorbate pairs are of great interest as NASA plans to use zeolite 13X in the next generation atmospheric revitalization system. Equilibrium isotherms describe a sorbent’s maximum capacity at a given temperature and adsorbate (<i>e.g.</i>, CO₂ or H₂O) partial pressure. New isotherm data from NASA Ames Research Center and NASA Marshall Space Flight Center for CO₂ and H₂O adsorption on zeolite 13X are presented. These measurements were carefully collected to eliminate sources of bias in previous data from the literature, where incomplete activation resulted in a reduced capacity. Several models are fit to the new equilibrium isotherm data and recommendations of the best model fit are made. The best-fit isotherm models from this analysis are used in all subsequent modeling efforts discussed in this dissertation.</div><div><br></div><div>The last two chapters examine the limitations of the axially disperse plug-flow model for predicting breakthrough in confined geometries. When a bed of pellets is confined in a rigid container, packing heterogeneities near the wall lead to faster flow around the periphery of the bed (<i>i.e.</i>, wall channeling). Wall-channeling effects have long been considered negligible for beds which hold more than 20 pellets across; however, the present work shows that neglecting wall-channeling effects on dispersion can yield significant errors in model predictions. There is a fundamental gap in understanding the mechanisms which control wall-channeling driven dispersion. Furthermore, there is currently no way to predict wall channeling effects a priori or even to identify what systems will be impacted by it. This dissertation aims to fill this gap using both experimental measurements and simulations to identify mechanisms which cause the plug-flow assumption to fail.</div><div><br></div><div>First, experimental evidence of wall-channeling in beds, even at large bed-to-pellet diameter ratios (<i>d</i>_bed/<i>d</i>_p=48) is presented. These experiments are then used to validate a method for accurately extracting mass transfer coefficients from data affected by significant wall channeling. The relative magnitudes of wall-channeling effects are shown to be a function of the adsorption/adsorbate pair and geometric confinement (<i>i.e.</i>, bed size). Ultimately, the axially disperse plug-flow model fails to capture the physics of breakthrough when nonplug-flow conditions prevail in the bed.</div><div><br></div><div>The final chapter of this dissertation develops a two-dimensional (2-D) adsorption model to examine the interplay of wall-channeling and adsorption kinetics and the adsorbent equilibrium capacity on breakthrough in confined geometries. The 2-D model incorporates the effect of radial variations in porosity on the velocity profile and is shown to accurately capture the effect of wall-channeling on adsorption behavior. The 2-D model is validated against experimental data, and then used to investigate whether capacity or adsorption kinetics cause certain adsorbates to exhibit more significant radial variations in concentration compared than others. This work explains channeling effects can vary for different adsorbate and/or adsorbent pairs—even under otherwise identical conditions—and highlights the importance of considering adsorption kinetics in addition to the traditional <i>d</i>_bed/<i>d</i>_p criteria.</div><div><br></div><div>This dissertation investigates key gaps in our understanding of fixed-bed adsorption. It will deliver insight into how these missing pieces impact the accuracy of predictive models and provide a means for reconciling these errors. The culmination of this work will be an accurate, predictive model that assists in the simulation-based design of the next-generation atmospheric revitalization system for humans’ journey to Mars.</div>

Scannende MEMS-Mikrospiegel stellen eine vielversprechende technologische Entwicklung mit potentiellen Anwendungen im Bereich der miniaturisierten Bildprojektion und Umgebungssensierung dar. Im Regelfall oszilliert das Spiegelelement hierbei resonant um die horizontale Achse, während die vertikale Achse statisch ausgelenkt wird. Somit ergibt sich ein sogenannter Raster-Scan. Während eine resonante Aktuierung in MEMS-Technologie im Frequenzbereich mehrerer kHz effizient umgesetzt werden kann, stellt die Implementierung statischer Antriebe eine Herausforderung dar. In dieser Arbeit wird ein neuartiges Aktuierungskonzept vorgestellt, das effizientere quasi-statische Auslenkung ermöglicht. Hierfür wird der Drehimpuls, der durch die hochfrequente horizontale Schwingung erzeugt wird, durch eine weitere resonante Oszillation ähnlicher Frequenz gestört, wodurch sich ein für die quasi-statische Auslenkung nutzbares Drehmoment ergibt. Da gyroskopische Effekte ausgenutzt werden, die nicht in aktuellen auf Modalanalyse basierenden Simulationsmethoden berücksichtigt sind, werden Starrkörper- und transiente FEM-Modelle entwickelt, um die Realisierbarkeit des Antriebskonzepts simulatorisch zu verifizieren. Im Rahmen der durch den genutzten Prozess gegebenen Randbedingungen werden daraufhin Aktuierungselemente für die resonanten Achsen erarbeitet und mit diesen zwei Designvarianten eines 2D-Mikrospiegels erstellt. Nach modellbasierter Verifikation werden diese in einer MEMS-Fertigungslinie prozessiert. Mit den generierten Mustern wird dann eine vollständige experimentelle Charakterisierung unter Nutzung eines speziell erstellten FPGA-basierten Evaluations-Boards durchgeführt. Beide Design-Varianten zeigen hierbei voll funktionsfähige Sensierungs- und Aktuierungselemente. Es kann ein erfolgreicher Nachweis der Funktionsfähigkeit des neuartigen Antriebskonzepts vollbracht werden. Die dabei gezeigte 2D-Projektion erreicht Winkel von 12° x 1.8° / Scanning MEMS micromirrors are an emergent technology for compact form factor image projection and environment sensing applications. Commonly the mirror element oscillates resonantly along the horizontal axis, whereas it is deflected statically along the vertical axis, performing a so called raster scan. While resonant actuation can be implemented efficiently in MEMS, static deflection however remains challenging. In this thesis a novel actuation concept for 2D MEMS micromirrors is introduced that potentially enables efficient quasi-static actuation. Therefore the angular momentum that is generated by the high frequency resonant axis is disturbed by an orthogonal resonant oscillation of similar frequency, leading to a torque that can be utilized to achieve an indirect quasi-static deflection. As in this case gyroscopic effects are exploited that are usually not considered in state of the art modal finite element based MEMS simulation, in order to validate the feasibility of the actuation concept rigid body and transient finite element based models are developed and simulation studies conducted. Using an existing manufacturing process as a framework, actuation schemes for the resonant axes are introduced and two distinct micromirror designs are developed and verified by simulation. These are processed in a MEMS manufacturing line. A thorough characterization study is then carried out using a custom FPGA based evaluation board with closed loop control capabilities. Both design variants are functional with regard to all actuation and tilt angle detection elements. A successful implementation of the proposed actuation concept is shown achieving 2D projection of a laser beam with tilt angles of 12 ◦ × 1.8 ◦ in frequency and amplitude controlled operation.

L’objet de la thèse est la modélisation de systèmes hétérogènes intégrant différents domaines de la physique et à signaux mixtes, numériques et analogiques (AMS). Une étude approfondie de différentes techniques d’extraction et de calibration de modèles comportementaux de composants analogiques à différents niveaux d’abstraction et de précision est présentée. Cette étude a mis en lumière trois approches principales qui ont été validées par la modélisation de plusieurs applications issues de divers domaines: un amplificateur faible bruit (LNA), un capteur chimique basé sur des ondes acoustiques de surface (SAW), le développement à plusieurs niveaux d’abstraction d’un capteur CMOS vidéo, et son intégration dans une plateforme industrielle. Les outils développés sont basés sur les extensions AMS du standard IEEE 1666 SystemC mais les techniques proposées sont facilement transposables à d’autres langages tels que VHDL-AMS ou Verilog-AMS utilisés en conception de dispositifs mixtes. / The thesis objective is the modeling of heterogeneous systems. Such systems integrate different physical domains (mechanical, chemical, optical or magnetic) therefore integrate analog and mixed- signal (AMS) parts. The aim is to provide a methodology based on high-level modeling for assisting both the design and the verification of AMS systems. A study on different techniques for extracting behavioral models of analog devices at different abstraction levels and computational weights is presented. Three approaches are identified and regrouped in three techniques. These techniques have been validated through the virtual prototyping of different applications issued from different domains: a low noise amplifier (LNA), a surface acoustic wave-based (SAW) chemical sensor, a CMOS video sensor with models developed at different abstraction levels and their integration within an industrial platform. The flows developed are based on the AMS extensions of the SystemC (IEEE 1666) standard but the methodologies can be implemented using other Analog Hardware Description Languages (VHDL-AMS, Verilog-AMS) typically used for mixed-signal microelectronics design.

Im Zuge der Miniaturisierung werden mechanische Nichtlinearitäten immer wichtiger für die Auslegung und Optimierung von mikromechanischen Drehratensensoren. Die vorliegende Arbeit beschäftigt sich mit neuen Simulationsmethoden zur Beschreibung dieser mechanischen Nichtlinearitäten. Die Methoden werden mit Benchmark-Simulationen und Messergebnissen validiert. Die Genauigkeit der neuen Simulationsmethoden erlaubt den Einsatz in der Designoptimierung von kommerziellen MEMS Drehratensensoren. / In this thesis, new simulation methods for the mechanical nonlinearities in microelectromechanical gyroscopes are developed and validated with benchmark simulations and experimental results. The benchmark simulations use transient finite element analysis that consider geometric nonlinear effects. Experimental results are from Laser Doppler Vibrometry and electrical measurements on wafer level. Two different simulation methods, the energy- and stiffness-based approach, are compared with respect to numerical performance and accuracy. In order to evaluate these methods, four different mechanical structures are taken into account: a doubly-clamped beam, a gyroscope test structure and two state-of-the-art gyroscopes with 1 and 2 axes. For the accuracy measurement, the simulated frequency shifts of modes are compared to the true frequency shifts that are developed from either benchmark simulation, Laser Doppler Vibrometry or electrical measurement. The presented methods allow to predict the frequency shift of modes accurately and with a minimum of computational cost. Furthermore, the methodologies allow to generate modal reduced order models which are compatible with common model order reduction in the field. This makes it possible to incorporate mechanical nonlinearity in already established reduced order models of gyroscopes. The simulation and modeling strategies are applicable for generic actuated structures that can be also in different fields of study such as the aerospace and earthquake engineering.