Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

This article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Kármán nonlinear strain–displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Kármán nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.This research is part of the NEMSPIEZO project, under funds from the French National Research Agency (Project ANR-08-NAN O-015-04), for which the authors are grateful

A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No \textit{a priori} knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM

POD Analysis of Cavity Flow Instability

A Mach 1.5 turbulent cavity flow develops large-amplitude oscillations, pressure drag and noise. This type of flow instability affects practical engineering applications, such as aircraft store bays. A simple model of the flow instability is sought towards developing a real-time model-based active control system for simple geometries, representative of open aircraft store bays. An explicit time marching second-order accurate finite-volume scheme has been used to generate time-dependent benchmark cavity flow data. Then, a simpler and leaner numerical predictor for the unsteady cavity pressure was developed, based on a Proper Orthogonal Decomposition of the benchmark data. The low order predictor gives pressure oscillations in good agreement with the benchmark CFD method. This result highlights the importance of large-scale phase-coherent structures in the Mach 1.5 turbulent cavity flow. At the selected test conditions, the significant pressure ‘energy’ content of these structures enabled an effective reduced order model of the cavity dynamic system. Directions and methods to further streamline and simplify the unsteady pressure predictor have been highlighted

Étude numérique et analyse physique du morphing électroactif pour des ailes et des profils hydrodynamiques à des écoulements turbulents à nombre de Reynolds élevé

La présente thèse étudie par simulation numérique et analyse physique les effets du morphing électroactif pour le design des ailes du futur permettant de réduire l’impact environnemental et d’accroître l’efficacité du transport aérien. La thèse examine les effets du morphing électroactif hybride. Ce concept consiste en une association de diverses classes d’actionneurs électroactifs opérant à des échelles de temps et de longueur multiples, en accord avec la dynamique du spectre turbulent et dans un contexte de bio-inspiration concernant l’actionnement des ailes, ailerons et plumes de grands oiseaux prédateurs. Le morphing électroactif hybride crée des modifications de la turbulence à de multiples échelles dans les zones cisaillées et le sillage proche et crée l’augmentation des performances aérodynamiques par l’action de mécanismes de rétroaction. La thèse effectue des simulations numériques à nombre de Reynolds élevé autour de configurations de profils d’aile et d’ailes d’avion supercritiques dans les régimes du bas subsonique correspondant aux phases du décollage et atterrissage, et transsonique correspondant au vol de croisière. Toutes les simulations sont effectuées par le code NSMB (Navier Stokes MultiBlock), en utilisant des approches de modélisation de la turbulence efficaces, permettant de prédire en accord avec les expériences physiques, le développement d’instabilités et de structures cohérentes gouvernant la dynamique des écoulements. Dans ce contexte, l’approche « Organized Eddy Simulation » (OES) a été employée et améliorée par des concepts de cascade inverse utilisant de la réinjection de la turbulence dans les zones fortement cisaillées. Cette méthode, basée sur un forçage stochastique des équations de transport turbulent a été étendue dans la présente thèse aux trois dimensions et ses bénéfices ont été quantifiés concernant l’évaluation des efforts aérodynamiques et le développement d’instabilités fluide. Les avantages de cette approche, qui a été introduite par ailleurs au sein de la « Detached Eddy Simulation », ont été étudiés concernant la prédiction du tremblement en régime transsonique et de l’interaction choc-couche limite. Les régimes du bas subsonique concernent les écoulements autour de profils et d’ailes de type A320 en configurations statiques et en morphing et sont étudiés en utilisant l’approche de modélisation OES également. Le morphing de la région proche du bord de fuite à l’aide de faibles déformations et de vibrations de fréquences dans le rang de 100-400 Hz a été étudié en synergie avec des résultats expérimentaux du projet Européen H2020 N° 723402 SMS : « Smart Moprhing and Sensing for Aeronautical configurations ». A l’aide d’une étude paramétrique détaillée, il a été mis en évidence que des combinaisons optimales de fréquence-amplitude de ces actionnements fournissent une augmentation drastique de la finesse aérodynamique. Ces effets ont été obtenus à l’aide de manipulation de la dynamique des interfaces « Turbulent - Non Turbulent » (TNT) et des interactions avec les interfaces « Turbulent- Turbulent » (TT). De plus, cette thèse a développé un modèle structural efficace permettant le contrôle de forme par des Alliages à Mémoire de Forme (AMF). Ces actionneurs permettent d’obtenir de grandes déformations à de basses fréquences en appliquant une grande cambrure de l’aile pour augmenter la portance et pour adapter la forme de l’aile aux différentes sollicitations aérodynamiques. La présente thèse propose un modèle efficace pour obtenir des formes-ciblées de configurations aérodynamiques utilisant des AMF embarqués. Un nouvel algorithme robuste a été développé et validé pour prédire la réponse non-linéaire de l’interaction AMF-structure. Cet algorithme a été couplé avec une méthode de prédiction de la structure et des paramètres opérationnels optimaux pour le design, fournissant ainsi des architectures de morphing plus performantes et réduisant l’impact environnementa

Haari lainikute meetod omavõnkumiste analüüsiks ja parameetrite määramiseks

Tala on konstruktsioonielement, mille ülesandeks on vastu pidada erinevatele koormustele. Projekteerimisel alahinnatud koormused, ebatäpsused tootmisel, söövitav keskkond, konstruktsiooni vananemine ekspluatatsiooni käigus võivad talasid kahjustada ning põhjustada kogu konstruktsiooni purunemist. Seetõttu talade dünaamilise käitumise modelleerimine ja ekspluatatsiooni jälgimine on jätkuvalt aktuaalne teema konstruktsioonide mehaanikas. Käesolev väitekiri on suunatud süstemaatilisele lähenemisele võnkumiste analüüsimiseks ja purunemise parameetrite määramiseks Euler-Bernoulli tüüpi talades. Töös pakutakse välja Haari lainikute meetod sageduste arvutamiseks ja andmete töötlemiseks. Nimelt, väitekirja esimeses osas on Haari lainikuid ja nende integreerimist rakendatud vabavõnkumise ülesannete korral, kus lahendatavaks võrrandiks on muutuvate kordajatega diferentsiaalvõrrand, millel puudub analüütiline lahend (näiteks ebaühtlase ristlõikega tala, materjali funktsionaalse gradientjaotusega tala). Arvutused kinnitasid, et pakutud lähenemisviis on kiire ja täpne vabavõnkumiste sageduste arvutamisel. Väitekirja teine osa käsitleb vabavõnkumisega seotud pöördülesandeid: pragude, delaminatsioonide, elastsete tugede jäikuse, massipunktide parameetrite määramist modaalsete omaduste kaudu. Kuna purunemise asukoha ja ulatuse arvutamine võnkumise diferentsiaalvõrrandist ei ole analüütiliselt võimalik, kasutatakse antud töös tehisnärvivõrke ja juhumetsi. Andmekogumite genereerimiseks lahendati võnkumise võrrand ning tulemusi töödeldi Haari lainikute abil. Arvutused näitasid, et Haari lainikute abil genereeritud andmekogumite arvutamiseks kuluv aeg oli üle kümne korra väiksem kui vabavõnkumiste sagedustele põhinevate andmekogumite arvutusaeg; Haari lainikute abil genereeritud andmekogumid ennustasid paremini purunemise asukohta, samas vabavõnkumiste sagedused olid tundlikumad purunemise ulatuse suhtes; enamikel juhtudel andsid tehisnärvivõrgud sama täpseid ennustusi kui juhumetsad. Töös pakutud meetodeid ja mudeleid saab kasutada teistes teoreetilistes ülesannetes vabavõnkumiste ja purunemiste uurimiseks või rakendada talade purunemise diagnostikas.A beam is a common structural element designed to resist loading. Underestimated loads during the design stage, looseness during the manufacturing stage, corrosive environment, collisions, fatigue may introduce some damage to beams. If no action is taken, the damage can turn into a fault or a breakdown of the whole system. Hereof, the entirety of beams is a crucial issue. This dissertation proposes a systematic approach to vibration analysis and damage quantification in the Euler-Bernoulli type beams. The solution is sought on the modal properties such as natural frequencies and mode shapes. The forward problem of the vibration analysis is solved using the Haar wavelets and their integration since the corresponding differential equations do not have an analytical solution. Multiple numerical examples indicate that the proposed approach is fast and accurate. Damage quantification (location and severity) of a crack, a delamination, a point mass or changes in the stiffness coefficients of elastic supports on the bases of the modal properties is an inverse problem. Since it is not analytically possible to calculate the damage parameters from the vibration differential equation, the task is solved with the aid of artificial neural networks or random forests. The datasets are generated solving the vibration equations and decomposing the mode shapes into the Haar wavelet coefficients. Multiple numerical examples indicate that the Haar wavelet based dataset is calculated more than ten times faster than the frequency based dataset; the Haar wavelets are more sensitive to the damage location, while the frequencies are more sensitive to the damage severity; in most cases, the neural networks produce as precise predictions as the random forests. The results presented in this dissertation can help in understanding the behaviour of more complex structures under similar conditions, provide apparent influence on the design concepts of structures as well as enable new possibilities for operational and maintenance concepts.https://www.ester.ee/record=b539883

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF PLASMA-JET FORMING

Sheet metal forming has found increasing applications in modern industries. To eliminate use of expensive tools during product development, thermal forming, a rapid prototyping process that is flexible enough to decrease costs has been developed. Thermal forming processes use a heat source to perform the required deformation mainly by creating a thermal difference along the thickness of the sheet. Gas flames, lasers and plasma heat sources have been used for sheet metal bending by thermal forming. An alternative to laser and gas flames, plasma-jet forming has been developed that uses a non-transferred plasma arc as a heat source. The plasma-jet forming system uses a highly controllable non-transferred plasma torch as a heat source to create the necessary thermal gradient in the sheet metal that causes the required plastic deformation. Various experiments to produce simple linear bends and other complex shapes have been conducted by using different scanning options and coupling techniques. A computer simulated model using finite element method is being developed to study key parameters affecting this process and also to measure the thermal transient temperature distribution during the process. A predictive model to relate the deformation to the temperature gradient for various materials is being developed. Simulation results that are in accordance to experimental observations will further improve this material forming process to be highly controllable and more accurat

Computational intelligent impact force modeling and monitoring in HISLO conditions for maximizing surface mining efficiency, safety, and health

Shovel-truck systems are the most widely employed excavation and material handling systems for surface mining operations. During this process, a high-impact shovel loading operation (HISLO) produces large forces that cause extreme whole body vibrations (WBV) that can severely affect the safety and health of haul truck operators. Previously developed solutions have failed to produce satisfactory results as the vibrations at the truck operator seat still exceed the “Extremely Uncomfortable Limits”. This study was a novel effort in developing deep learning-based solution to the HISLO problem. This research study developed a rigorous mathematical model and a 3D virtual simulation model to capture the dynamic impact force for a multi-pass shovel loading operation. The research further involved the application of artificial intelligence and machine learning for implementing the impact force detection in real time. Experimental results showed the impact force magnitudes of 571 kN and 422 kN, for the first and second shovel pass, respectively, through an accurate representation of HISLO with continuous flow modelling using FEA-DEM coupled methodology. The novel ‘DeepImpact’ model, showed an exceptional performance, giving an R2, RMSE, and MAE values of 0.9948, 10.750, and 6.33, respectively, during the model validation. This research was a pioneering effort for advancing knowledge and frontiers in addressing the WBV challenges in deploying heavy mining machinery in safe and healthy large surface mining environments. The smart and intelligent real-time monitoring system from this study, along with process optimization, minimizes the impact force on truck surface, which in turn reduces the level of vibration on the operator, thus leading to a safer and healthier working mining environments --Abstract, page iii

Dynamic analysis of assembled structures with nonlinearity

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Development of Reaction Discovery Tools in Photochemistry and Condensed Phases

Photochemistry obeys different rules than ground-state chemistry and by doing so opens avenues for synthesis and materials properties. However, the different rules of photochemistry make understanding the fine details of photochemical reactions difficult. Computational chemistry can provide the details for understanding photochemical reactions, but the field of computational photochemistry is still new, and many techniques developed for ground-state reactions are not directly applicable to photochemical reactions. As a result, many photochemical mechanisms are not understood, and this hinders the rational design and synthesis of new photochemistry. To address this need, this thesis develops techniques to search for and study photochemical reactions. Chapter 2 and 3 develop methods to calculate photochemical reactions in gas- and condensed-phases via minimum energy reaction paths. First, Chapter 2 develops a method to search the molecular 3N-6 space for photochemical reactions. This space, although vast, is not chaotic and can be efficiently searched using a concept familiar to chemists: breaking and adding bonds and driving angles and torsions. Furthermore, this procedure can be automated to predict new chemistry not previously identified by experiments. Chapter 3 furthers this research by leveraging the concept of molecules to enable the computational study of reactions in large multi-molecular systems like crystals. Specifically, the use of a new coordinate system involving translational and rotational coordinates allows decoupling of the coordinate systems of the individual molecules, which is necessary for the efficient algebra. Importantly, these methods are general, they can be used to study single molecules and crystals, and much in between. These methods are demonstrated on complex chemical problems including the isomerization pathways of ethylene and stilbene (Chapter 2), the photocycloaddition of butadiene (Chapter 2), the rotation of a crystalline gyroscope (Chapter 3), the bicycle pedal rotation of cis,cis-diphenylbutadiene (Chapter 4), and the mechanism of a reversible photoacid (Chapter 5). These problems have value in understanding the processes of vision, optomechanics, and high-energy materials, and through their xx study much needed insight is gained that can be useful for designing new syntheses and materials. Furthermore, the new computational methods open the possibility for many future investigations. The results of Chapter 2 find a novel roaming-atom and hula-twist isomerization pathway and use automated reaction discovery tools to identify a missing butadiene photoproduct and why the [4+2] cycloaddition is forbidden. The results of Chapter 3 and 4 build on Chapter 2 by including the influence of a steric environment. Chapter 3 demonstrates by application to a molecular gyroscope that extreme long-range correlated motion can be captured with GSM, and Chapter 4 details how the one-bond flip and hula-twist mechanisms are suppressed by the crystal cavity, the nature of the seam space in steric environments, and the features of the bicycle pedal mechanism. For example, the bicycle pedals rotate through the passageway in the adjacent monomers. However, the models do not capture the quantitative activation barriers and more work is needed. Finally, Chapter 5 provides the ultrafast details of how the photoacid isomerizes and ring-closes with experimental and computational evidence. Unfortunately, quantitative calculation of pKa cannot be provided with the computations employed herein. In summary, this thesis provides an advancement in the knowledge of photochemical mechanisms that can be used for the development of new syntheses and offers new tools with capacity to study complex photochemical problems.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163005/1/craldaz_1.pd