<p>When a design feature (such as material choice, internal bracing pattern, guitar body depth, and sound hole diameter) of an acoustic guitar changes, the effect of the change on the guitar’s sound is not well understood. As a result, luthiers approximate how to make guitars that have resonant frequencies of around 95-105 Hertz (Hz), the frequency range which sounds “good.” The researcher designed a reconfigurable fixture that simulated an acoustic guitar body with a variable body depth and sound hole diameter. The researcher used this testing fixture to examine the relationship between sound hole diameter, body depth, and resonant frequency. She conducted an experimental parameter sweep, measuring frequency response functions (FRFs) to collect data on the first, Helmholtz, and second resonant frequencies of the simulated acoustic guitar. The researcher pinpointed the general trends in the correlation between resonant frequency, body depth, and sound hole diameter using the frequency data from the FRF measurements. She determined that as sound hole diameter increased, the first, Helmholtz, and second resonant frequencies increased; and as body depth and body volume increased, the first and Helmholtz resonant frequencies decreased, while the second resonant frequency increased up until a body depth of approximately 4.50” inches. Exploring alternative design features and material choices contributes to improving urban infrastructure by encouraging luthiers to make instruments with sustainable materials (National Academy of Engineering, Grand Challenges – Restore and Improve Urban Infrastructure, 2023).</p>

<p>The vehicle industry has an endless appetite to get better. Often, this appetite is justified by the need of the hour. In the agricultural space, this translates to improving agricultural productivity in the face of population growth, reduced arable land and shortage of skilled farm labor. As for torsional vibrations, which have been around ever since the wheel was invented, the problem gets redefined with new regulations demanding new powertrains with improved fuel efficiency and reduced emissions.</p><p>A solution to the agriculture problem, involves efficiently automating the harvesting process.The first section of this thesis covers the ‘Auto-Unload’ where the goal of automation is achieved. This was done by building a simulation framework that was used to develop and synthesize the ‘AutoUnload’ controller. This controller was later deployed on a combine and a successful unloading on-the-go was demonstrated with a combine, tractor, and tractor-driven grain cart.</p><p>The solution to the second problem about drivetrain vibrations involved deriving a mathematical model for simulating the powertrain of a medium-duty truck. This was done to confirm resonance seen during testing done on a chassis dynamometer. The consequent control strategy to mitigate undesired vibration was to move the torque excitation away from the natural frequency of the system. This was achieved by a ‘gear-shifting’ algorithm. Comparison between on-road tests with and without the ‘gear-shifting’ algorithm showed that such a control strategy can effectively eliminate resonance. The solution methodology developed in this work is robust and transferable to higher engine torques and harvest speeds.</p>

Smart structure control systems commonly use piezoceramic sensors or accelerometers as vibration measurement devices. These measurement devices often produce noisy and/or low-precision signals, which makes it difficult to measure small-amplitude vibrations. Laser interferometry devices pose as an alternative high-precision position measurement method, capable of nanometer-scale resolution. The aim of this research is to utilize a model-based design approach to develop and implement a real-time Linear Quadratic Gaussian (LQG) regulator for a piezoelectric actuated smart structure using a high-precision laser interferometry measurement system to suppress the excitation of vibratory modes. The analytical model of the smart structure is derived using the extended Hamilton Principle and Euler-Bernoulli beam theory, and the equations of motion for the system are constructed using the assumed-modes method. The analytical model is organized in state-space form, in which the effects of a low-pass filter and sampling of the digital control system are also accounted for. The analytical model is subsequently validated against a finite-element model in Abaqus, a lumped parameter model in Simscape Multibody, and experimental modal analysis using the physical system. A discrete-time proportional-derivative (PD) controller is designed in a heuristic fashion to serve as a baseline performance criterion for the LQG regulator. The Kalman Filter observer and Linear Quadratic Regulator (LQR) components of the LQG regulator are also derived from the state-space model. It is found that the behavior of the analytical model closely matches that of the physical system, and the performance of the LQG regulator exceeds that of the PD controller. The LQG regulator demonstrated quality estimation of the state variables of the system and further constitutes an exceptional closed-loop control system for active vibration control and disturbance rejection of the smart structure.

The transition from internal combustion engine to battery electric cars is accompanied by a shift on the NVH issues damaging the passenger comfort. The rolling noise generated by the wheels and tyres is in particular characterized by an increasing attention from OEMs and car manufacturers. Among the causes of the rolling noise are the vibrations generated at the wheel, which are transmitted to the vehicle interior through its structure. To limit these vibrations at their source, a new innovative concept has been proposed at Stellantis. This idea is based on the use of a specific type of vibration absorber known by the acronym MTMD (Multiple Tuned Mass Damper).First, the existing literature about vibrations absorbers and optimisation techniques has been reviewed. Then, initial simulations on a global model comprising the wheel and beam-like resonators have shown how this system can effectively reduce a resonant peak.Optimisation processes have then revealed an important attenuation of a wheel resonance, even when the peak frequency is shifted. This demonstrated how important the distribution of resonators resonance frequencies are and their damping ratios when designing a robust and efficient MTMD.Finally, local resonators have been designed and modelled by considering the constraints for an integration on a wheel. A satisfactory design for resonators able to vibrate at the wanted frequency has been found. The beam-like resonators used in the first global model have then been replaced by these real resonators, confirming the possible gain with this device in a vehicle. / Övergången från förbränningsmotorer till batterielektriska bilar åtföljs av en övergång till NVH-frågor som kan påverka passagerarnas komfort. Det rullningsljud som genereras av hjul och däck får i synnerhet ökad uppmärksamhet från OEM:er och biltillverkare.Bland orsakerna till rullningsljudet finns de vibrationer som genereras vid hjulet och som överförs till fordonets inre genom dess struktur. För att begränsa dessa vibrationer vid källan har ett nytt innovativt koncept föreslagits av Stellantis. Idén bygger på användningen av en särskild typ av vibrationsdämpare som kallas MTMD (Multiple Tuned Mass Damper).Först har den befintliga litteraturen om vibrationsdämpare och optimeringstekniker gåtts igenom. Därefter har inledande simuleringar på en global modell som omfattar hjulet och balkliknande resonatorer visat hur detta system effektivt kan minska en resonanstopp.Optimeringsprocesserna har sedan bekräftat att hjulresonansen är kraftigt dämpad, även när toppfrekvensen är förskjuten. Detta visade hur viktig fördelningen av resonansfrekvenser och dämpningsförhållanden för resonatorer är när man utformar en robust och effektiv MTMD.Slutligen har lokala resonatorer utformats och modellerats genom att beakta begränsningarna för en integrering i ett hjul. En tillfredsställande utformning av resonatorer som kan vibrera vid den önskade frekvensen har hittats. De balkliknande resonatorer som användes i den första globala modellen har sedan ersatts av dessa riktiga resonatorer, vilket bekräftar den potentiella förbättringen med denna anordning i ett fordon.

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Orientador: Edvaldo Assunção / Resumo: Neste trabalho é proposta a resolução do problema do regulador linear quadrático (Linear Quadratic Regulator - LQR) via desigualdades matriciais lineares (Linear Matrix Inequalities - LMIs) para sistemas lineares e invariantes no tempo sujeitos a incertezas politópicas, bem como para sistemas lineares sujeitos a parâmetros variantes no tempo (Linear Parameter Varying - LPV). O projeto dos controladores é baseado na realimentação derivativa. A escolha da realimentação derivativa se dá devido à sua fácil implementação em certas aplicações como, por exemplo, no controle de vibrações. Os sinais usados na realimentação são aceleração e velocidade, sendo obtidos por meio de acelerômetros. Por meio do método proposto é possível obter condições LMIs para a síntese de controladores que garantam a estabilização do sistema em malha fechada, sendo que os controladores possuem desempenho otimizado. Para a formulação das condições LMIs, uma função de Lyapunov do tipo quadrática é utilizada. Exemplos teóricos e simulações são utilizados como forma de validação dos métodos propostos, além de mostrar que os novos resultados apresentam condições menos conservadoras. Além disso, ao final é apresentada uma implementação prática em um sistema de suspensão ativa, produzida pela Quanser®. / Abstract: The resolution of linear quadratic regulator (LQR) problem via linear matrix inequalities (LMIs) for linear time-invariant systems subject to polytopic uncertainties, as linear systems subjects to linear parameter varying (LPV), is proposed in this work. The controllers' designs are based on the state derivative feedback. The aim to the choice of the state derivative feedback is your easy implementation in a class of mechanical systems, such as in vibration control, for example. The signals used for feedback are acceleration and velocity, it is obtained by means of accelerometers. Through the proposed method it is possible to obtain LMIs conditions for the synthesis of controllers that guarantee the stabilisation of the closed-loop system, being that the controllers have optimised performance. For the LMIs conditions formulations, a Lyapunov function of type quadratic is used. As a form of validation, theoretical examples and simulations are performed, besides to show that the new results are less conservative. Furthermore, a practical implementation in an active suspension system, produced by Quanser®, is performed. / Mestre

Smart materials is an active research area devoted to the design of structured materials showingphysical properties that can be modified in response to an external stimulus.This study focuses on the analysis and design of adaptive system for vibroacoustic control. Theresearch investigates the design of a active interface made of piezoelectric transducers arranged ina two-dimensional lattice. Each transducer is individually shunted to an external electric circuitsynthesizing a negative capacitance effect. It allows to control waves propagating inside a structuretaking advantage of the multi-field coupling between the structural plate and the electrical circuitsshunting the piezoelectric patches.The performance of the metacomposite has been evaluated through numerous numerical andexperimental tests. The smart wave-guide has been analyzed by using the Bloch theorem appliedto two-dimensional piezo-elastic systems. Subsequently an optimization procedure has been usedwith the purpose to select the most appropriate set of circuit's parameters.A prototype of the smart waveguide has been manufactured and tested. The results results clearlyshow the filtering and attenuating capabilities of this device.Finally a finite element model of the finite extent smart plate has been considered in order toasses the robustness of the proposed control strategy respect to a modification of the circuit'sparameters, the topology of the active interface and the properties of the controlled plate.A brief review conclude the work delineating which aspects of the design should be modified inorder to obtain a device suitable for industrial applications.

Cette thèse s’interesse au contrôle des flux d’énergie mécanique dans les structures périodiques. Les problèmes de dynamiques des structures considérés dans cette thèse sont abordés sous l'angle d'une description ondulatoire : la réponse forcée d’un système est calculée comme une superposition d’ondes dans la structure, tandis que les modes propres sont interprétés comme des ondes stationnaires.Un des avantages de l’approche ondulatoire est qu’elle permet de réduire de manière importante la taille des problèmes de dynamique. Ceci se révèle particulièrement utile dans le domaine des hautes et moyennes fréquences, où les calculs par éléments finis deviennent très coûteux en temps à cause du grand nombre de degrés de liberté nécessaire à la convergence du modèle. Afin de contourner ce problème, cette thèse s'appuie sur la méthode des éléments finis ondulatoires (Wave Finite Element Method (WFEM)). Une des principales améliorations proposées est l’utilisation de plusieurs méthodes de synthèses modales (Component Mode Synthesis (CMS)) pour accélérer l’analyse des guides d’ondes généraux en présence d’amortissement ou de matériaux piézo-électriques. Les erreurs numériques restent faibles du fait de l’utilisation d'une base de projection réduite constituée d'ondes propagatives. Une autre contribution est le procédé de modélisation multi-échelle pour les assemblages de structures périodiques et non-périodiques. L’idée principale est de modéliser les parties non-périodiques par la méthode des éléments finis, et les parties périodiques par WFEM. Les interactions entre les différentes sous-structures sont modélisées par des coefficients de réflexion ou des impédances mécaniques. Ces travaux réalisent une extension de la WFEM à des structures plus complexes et plus proches des applications industrielles. Un autre intérêt de la vision ondulatoire est qu’elle mène à de nouvelles idées pour le contrôle des vibrations. Dans cette thèse, des matériaux piézo-électriques et des circuits de shunt, distribués de façon périodique sont utilisés afin de modifier artificiellement la propagation des ondes grâce au couplage électromécanique. Un nouveau critère, nommé « Wave Electromechanical Coupling Factor (WEMCF) », est proposé pour évaluer, en termes énergétiques, l’intensité du couplage entre le champ électrique et le champ mécanique lors du passage d'une onde. Ce facteur peut être obtenu à partir des caractéristiques ondulatoires obtenues par la WFEM. On montre que le WEMCF est fortement lié à l'atténuation dans le guide d’ondes piézo-électrique. La conception des paramètres géométriques et électriques peut être ainsi être effectuée séparément. Ce principe est appliqué à la réduction des vibrations d’une poutre encastrée. Le WEMCF est utilisé comme fonction objectif pour l'optimisation durant la conception géométrique, la masse totale de matériau piézo-électriques étant contrainte. Un circuit à capacité négative est utilisé pour élargir le band-gap de Bragg. La stabilité du système est prise en compte comme une contrainte sur la valeur de cette capacité. Les vibrations sont localisées et facilement dissipées par l’introduction d’absorbeurs sur la frontière. Ce procédé de conception basée sur une approche ondulatoire aboutit à des solutions stables, légères, et insensibles aux conditions aux limites dans une large gamme de fréquence. Par conséquent, il est prometteur pour analyser les structures en moyenne et haute fréquence où il est difficile d’accéder aux informations modales exactes. / This thesis describes analysis and control approaches for the vibration and energy flow through periodic structures. The wave description is mainly used to address the structural dynamic problems considered in the thesis: forced response is calculated as the superposition of the wave motions; natural modes are understood as standing waves induced by the propagating waves that recover to the same phase after traveling a whole circle of the finite structure. One advantage of the wave description is that they can remarkably reduce the dimensions of structural dynamic problems. This feature is especially useful in mid- and high frequencies where directly computing the full Finite Element Method (FEM) model is rather time-consuming because of the enormous number of degree-of-freedoms. This thesis extends one widely used wave-based numerical tool termed Wave Finite Element Method (WFEM). The major improvements are the use of several Component Mode Synthesis (CMS) methods to accelerate the analysis for general waveguides with proportional damping or piezoelectric waveguides. The numerical error is reduced by using the proposed eigenvalue schemes, the left eigenvectors and the reduced wave basis. Another contribution is the multi-scale modeling approach for the built-up structures with both periodic and non-periodic parts. The main idea is to model the non-periodic parts by FEM, and model the periodic parts by WFEM. By interfacing different substructures as reflection coefficients or mechanical impedance, the response of the waveguide is calculated in terms of different scales. These two contributions extend WFEM to more complex structures and to more realistic models of the engineering applications.Another benefit of the wave perception is that it leads to new ideas for vibration control. In this thesis periodically distributed piezoelectric materials and shunt circuit are used to artificially modify the wave properties by electric impedance. A novel metrics termed the Wave Electromechanical Coupling Factor (WEMCF) is proposed, to quantitatively evaluate the coupling strength between the electric and mechanical fields during the passage of a wave. This factor can be post-processed from the wave characteristics obtained from WFEM through an energy formula. We show that WEMCF is strongly correlated to the best performance of the piezoelectric waveguide. Hence the design for the geometric and electric parameters can be done separately. An application is given, concerning the vibration reduction of a cantilever beam. WEMCF is used as an optimization objective during the geometric design, when the overall mass of the piezoelectric materials is constrained. Then the negative capacitance is used with a stability consideration to enlarge the Bragg band gap. The vibration is localized and efficiently dissipated by few boundary dampers. The wave-based design process yields several broadband, stable, lightweight and boundary condition insensitive solutions. Therefore, it is promising at mid- and high frequencies where exact modal information is difficult to access.

This research investigates on-blade partial span active plain trailing edge flaps (TEFs)with an aim to alleviate the helicopter vibrations. Among all the available smart materials, piezoelectric stack actuator(PEA)has shown its strong candidature for full scale rotor systems. Although, PEAs are quite robust in operation, however, they exhibit rate dependent hysteresis phenomenon and can generate only very small displacements. Dynamic hysteresis is a complex phenomenon which, if not modeled, can lead to drift in the vibration predictions. In this research, a comprehensive experimental analysis is performed on a commercially available piezostack actuator, APA-500L, which is well suited for full scale applications. Rate dependent hysteresis loops are obtained for helicopter operational frequencies. Nonlinear rate-dependent hysteresis loops are modeled using conic section approach and the results are validated with experimental data. Dynamic hysteresis exhibited by the PEA is further cascaded with the helicopter aeroelastic analysis and its effect on helicopter vibration predictions is investigated. PEAs generate high force but are limited by small translational motions. A linear to rotary motion amplification mechanism is required to actuate the TEF for vibration alleviation. A smart flap is designed and developed using computer-aided-design models. A rotor blade test section is fabricated and a lever-fulcrum mechanism (AM-1) is developed for a feasibility study. Smart flap actuation is demonstrated on the rotor blade test section. The conventional motion amplification devices contain several linkages, which are potential sites for structural failure. A novel pinned-pinned post-buckled beam linear-to-rotary motion amplifier (AM-2) is designed and developed to actuate the flaps. A new design of linear-to-linear amplification mechanism (LX-4) is developed and is employed in conjunction with AM-2 to increase the flap angles by an order of magnitude. An analytical model is developed using Mathieu-Hill type differential equations. Static and dynamic tests are conducted on a scaled flap model. Helicopter aeroelastic simulations show substantial reduction in hub loads using AM-2 mechanism. To further enhance the flap angles, an optimization study is performed and optimal beam dimensions are obtained. A new technique is also proposed to actively bias the flaps for both upward and downward motion. Critical flap design parameters, such as flap span, flap chord and flap location influences the flap power requirement and vibration objective function significantly. A comprehensive parametric investigation is performed to obtain the best design of TEFs at various advance ratios. Although, parametric study equips the designer with vital information about various critical system parameters, however, it is a computationally expensive exercise especially when used with large comprehensive helicopter aero elastic codes. A formal optimization procedure is employed to obtain the optimal flap design and location. Surrogate models are developed using design of experiments based on response surface methodology. Two new orthogonal arrays are proposed to construct the second order polynomial response surfaces. Pareto analysis is employed in conjunction with a newly developed computationally efficient evolutionary multi-objective bat algorithm. Optimal flap design and flap locations for dual trailing edge flaps are obtained for mutually conflicting objectives of minimum vibration levels and minimum power requirement to actuate the flaps.

<p> There is a current interest in exploring novel microstructural architectures that take advantage of the response of independent phases. Current guidelines in materials design are not just based on changing the properties of the different phases but also on modifying its base architecture. Hence, the mechanical behavior of composite materials can be adjusted by designing microstructures that alternate stiff and flexible constituents, combined with well-designed architectures. One source of inspiration to achieve these designs is Nature, where biologically mineralized composites can be taken as an example for the design of next-generation structural materials due to their low density, high-strength, and toughness currently unmatched by engineering technologies.</p><p><br></p> <p>The present work focuses on the modeling of biologically inspired composites, where the source of inspiration is the dactyl club of the Stomatopod. Particularly, we built computational models for different regions of the dactyl club, namely: periodic and impact regions. Thus, this research aimed to analyze the effect of microstructure present in the impact and periodic regions in the impact resistance associated with the materials present in the appendage of stomatopods. The main contributions of this work are twofold. First, we built a model that helped to study wave propagation in the periodic region. This helped to identify possible bandgaps and their influence on the wave propagation through the material. Later on, we extended what we learned from this material to study the bandgap tuning in bioinspired composites. Second, we helped to unveil new microstructural features in the impact region of the dactyl club. Specifically, the sinusoidally helicoidal composite and bicontinuous particulate layer. For these, structural features we developed finite element models to understand their mechanical behavior.</p><p><br></p> <p>The results in this work help to elucidate some new microstructures and present some guidelines in the design of architectured materials. By combining the current synthesis and advanced manufacturing methods with design elements from these biological structures we can realize potential blueprints for a new generation of advanced materials with a broad range of applications. Some of the possible applications include impact- and vibration-resistant coatings for buildings, body armors, aircraft, and automobiles, as well as in abrasion- and impact-resistant wind turbines.</p><br>