The Meshless Local Petrov-Galerkin (MLPG) method has been employed to analyze the following linear and nonlinear solid mechanics problems: free and forced vibrations of a segmented bar and a cracked beam, pull-in instability of an electrostatically actuated microbeam, and plane strain deformations of incompressible hyperelastic materials. The Moving Least Squares (MLS) approximation is used to generate basis functions for the trial solution, and for the test functions. Local symmetric weak formulations are derived, and the displacement boundary conditions are enforced by the method of Lagrange multipliers. Three different techniques are employed to enforce continuity conditions at the material interfaces: Lagrange multipliers, jump functions, and MLS basis functions with discontinuous derivatives. For the electromechanical problem, the pull-in voltage and the corresponding deflection are extracted by combining the MLPG method with the displacement iteration pull-in extraction algorithm. The analysis of large deformations of incompressible hyperelastic materials is performed by using a mixed pressure-displacement formulation. For every problem studied, computed results are found to compare well with those obtained either analytically or by the Finite Element Method (FEM). For the same accuracy, the MLPG method requires fewer nodes but more CPU time than the FEM. / Ph. D.

This thesis concerns itself with a finite element model of nonproportional viscoelastic damping and its subsequent reduction. The Golla-Hughes-McTavish viscoelastic finite element has been shown to be an effective tool in modeling viscoelastic damping. Unlike previous models, it incorporates physical data into the model in the form of a curve fit of the complex modulus. This curve fit is expressed by minioscillators. The frequency dependence of the complex modulus is accounted for by the addition of internal, or dissipation, coordinates. The dissipation coordinates make the viscoelastic model several times larger than the original. The trade off for more accurate modeling of viscoelasticity is increased model size. Internally balanced model order reduction reduces the order of a state space model by considering the controllability/observability of each state. By definition, a model is internally balanced if its controllability and observability grammians are equal and diagonal. The grammians serve as a ranking of the controllability/observability of the states. The system can then be partitioned into most and least controllable/observable states; the latter can be statically reduced out of the system. The resulting model is smaller, but the transformed coordinates bear little resemblance to the original coordinates. A transformation matrix exists that transforms the reduced model back into original coordinates, and it is a subset of the transformation matrix leading to the balanced model. This whole procedure will be referred to as Yae's method within this thesis. By combining GHM and Yae's method, a finite element code results that models nonproportional viscoelastic damping of a clamped-free, homogeneous, Euler-Bernoulli beam, and is of a size comparable to the original elastic finite element model. The modal data before reduction compares well with published GHM results, and the modal data from the reduced model compares well with both. The error between the impulse response before and after reduction is negligible. The limitation of the code is that it cannot model sandwich beam behavior because it is based on Euler-Bernoulli beam theory; it can, however, model a purely viscoelastic beam. The same method, though, can be applied to more sophisticated beam models. Inaccurate results occur when modes with frequencies beyond the range covered by the curve fit appear in the model, or when poor data are used. For good data, and within the range modeled by the curve fit, the code gives accurate modal data and good impulse response predictions. / Master of Science

Energy efficient appliances and devices are becoming increasingly necessary as emissions from electricity production continue to increase the severity of global warming. Many of such appliances have not been substantially redesigned since their creation in the early 1900s. One device in particular which has arguably changed the least and consumes the most energy during use is the electric clothes dryer. The common form of this technology in the United States relies on the generation of thermal energy by passing electrical current through a metal. The resulting heat causes liquid within the clothing to evaporate where humid air is ejected from the control volume. While the conversion of energy from electrical to thermal through a heating element is efficient, the drying characteristics of fabrics in a warm humid environment are not, and much of the heat inside of the dryer does not perform work efficiently. In 2016, researchers at Oak Ridge National Laboratory in Knoxville, Tennessee, proposed an alternative mechanic for the drying of clothes which circumvents the need for thermal energy. This method is called direct-contact ultrasonic clothes drying, utilizing atomization through direct mechanical coupling between mesh piezoelectric transducers and wet fabric. During the atomization process, vertical oscillations of a contained liquid, called Faraday excitations, result in the formation of standing waves on the liquid surface. At increasing amplitudes and frequencies of oscillation, wave peaks become extended and form "necks" connecting small secondary droplets to the bulk liquid. When the oscillation reaches an acceleration threshold, the droplet momentum is sufficient to break the surface tension of the neck and enable the droplets to travel away from the liquid. For smaller drops where surface tension is high, a larger magnitude of acceleration is needed to reach the critical neck lengths necessary for droplet ejection. The various pore sizes within the many fabrics comprising our clothing results in many sizes of droplets retained by the fabric, affecting the rate of atomization due to the differences in surface tension. In this study, we will investigate the physical processes related to the direct contact ultrasonic drying process. Beginning with the electrical actuation of the transducer used in the world's first prototype dryer, we will develop an electromechanical model for predicting the resulting deformation. Various considerations for the material properties and geometry of the transducer will be made for optimizing the output acceleration of the device. Next, the drying rates of fabrics in contact with the transducer will be modeled for identification of parameters which will facilitate timely and energy efficient drying. This task will identify the first ever mechanically coupled drying equation for fabrics in contact with ultrasonic vibrations. The ejection rate of the water atomized by the transducer and passed through microchannels to facilitate drying will then be physically investigated to determine characteristics which may improve mass transport. Finally, future considerations and recommendations for the development of ultrasonic drying will be made as a result of the insight gained by this investigation. / Doctor of Philosophy / Energy efficient appliances and devices are becoming increasingly necessary as emissions from electricity production continue to increase the severity of global warming. Many of such appliances have not been substantially redesigned since their creation in the early 1900s. One device in particular which has arguably changed the least and consumes the most energy during use is the electric clothes dryer. The common form of this technology in the United States relies on the generation of thermal energy by passing electrical current through a metal. The resulting heat causes liquid within the clothing to evaporate where the humid air is ejected from the control volume. While the conversion of energy from electrical to thermal through a heating element is efficient, the drying characteristics of fabrics in a warm humid environment are not, and much of the heat inside of the volume does not perform drying as efficiently as possible. In 2016, researchers at Oak Ridge National Laboratory in Knoxville, Tennessee, proposed an alternative mechanism for the drying of clothes which circumvents the need for thermal energy. This method is called direct-contact ultrasonic clothes drying, and utilizes a vibrating disk made of piezoelectric and metal materials to physically turn the water retained in clothing into a mist, which can be vented away leaving behind dry fabric. This method results in the water leaving the fabric at room temperature, rather than being heated, which bypasses the need for a substantial amount of energy to convert from the liquid to gas phase. The first ever prototype dryer shows the potential of being twice as efficient as conventional dryers. This investigation is based around improving the device atomizing the water within the clothing, as well as understanding physical processes behind the ultrasonic drying process. These tasks will be conducted through experimental measurements and mathematical models to predict the behavior of the atomizing device, as well as computer software for both the parameters experimentally measured, and items which cannot be measured such as the flow in very small channels. The conclusions of this study will be recommendations for the future development of direct contact ultrasonic drying technology.

Several areas of research regarding floor vibrations were studied during the process of this research. A basic literature review of previous work in the field of floor vibrations is presented along with a summary of the study. The first area of study involved a comparison of finite element models with field tests for a suspended floor system. The suspended floor system underwent several retrofits to determine which retrofit reduced annoying vibrations the most. Comparisons were also made to see how well a finite element model could be used to predict the effectiveness of the retrofits. The attempt to make accurate finite element models was successful. The second area of study involved an experimental modal analysis (EMA). The experimental mode shape was compared with that from the finite element model (FEM). The research done in this area of study also involved measuring damping for a suspended floor system. The floor system was also subjected to a known input force and the response of the system was compared to the theoretical response based on the finite element model and the hand calculations prescribed by AISC Design Guide 11–Floor Vibrations Due to Human Activity (Murray et al., 1997). The findings helped provide useful information for the third area of study. The third area of this study focused on finding a method for performing a quick and inexpensive field test on a floor system to determine its acceptability. No good method found. The fourth area of this study was to find a way to accurately model complex floor systems with finite element modeling programs. Previous research yielded good results in the area of frequency prediction. However, the main focus of this study was to find a way to accurately predict peak acceleration of a complex floor system. This portion of research did not find a way to model complex floor systems in a finite element program for producing accurate peak accelerations. However, the source of error between the finite element program and the hand calculations was accurately defined. / Master of Science

The scope of this study is divided into three topics. To begin, more accurate methods for estimating the fundamental natural frequencies of floors were explored. Improvements for predicting the behavior of floor systems using several criteria were also investigated. The final topic compared the AISC and SCI methods for analyzing vibrations acceptability. Natural frequency prediction was studied by examining 103 case studies involving floor systems of various framing occupied or being constructed in the United States and Europe. Based on the results from these comparisons, it was reasonably concluded that the predicted bay frequency using Dunkerly's estimate (fn2) is not the most accurate method for predicting the system frequency using the AISC Design Guide for all types of framing analyzed. The predicted beam frequency using AISC methods provided sound correlations with the measured bay frequencies. On the other hand, with the exception of floor systems with joist girders and joists, the results showed that the SCI methods provided more accurate predictions of bay frequency despite a fair amount of data scatter. Evaluations based on the AISC Design Guide 11, the SCI criteria Murray Criterion, and Modified Reiher-Meister scale were compared with subjective field analyses for each case study in the second part of this study. The AISC Design Guide criterion is the most consistent method for predicting floor behavior. The SCI criterion is the next most consistent method for floor acceptability, followed by the Murray Criterion then the Modified Reiher-Meister scale. In the final part of this study, predicted accelerations and floor behavior tolerability for 78 case studies were evaluated using the AISC and the SCI criteria. The two prediction methods are in agreement for 82 % (64 of 78) of the case studies, and strongly disagree for only 12 % (9 of 78) of the case studies. / Master of Science

The primary purpose of this study is to evaluate the use of Doppler Lidar sensors for assessing track weakening that would indicate early stages of track instability. Such track weakening could lead to gage widening or track buckling due to rail thermal expansion. A series of tests are performed at the Transportation Technology Center's High Tonnage Loop, where two sections of track are "doctored" to have weaker lateral strength, one on a tangent and another one in a curve. Multiple tests are performed at speeds ranging from 10 – 40 mph, during which the lateral and vertical deflections of the rail are measured under the weight of the passing wheels of a heavily-loaded gondola. The track weakness is created by removing the rail spikes from eight consecutive ties. The measurements from the soft sections are compared with a track section on a tangent that is determined to have nominally sufficient ("good") stiffness. The measurement system consists of four Doppler Lidar units, two oriented toward the rail gage face to measure lateral rail movement, and two directed to the top of the rail to measure vertical rail movement. The combination of the vertical and lateral measurements is used as an indicator of a lack of rail stability if larger-than-normal movement of the rail is detected in either direction. The data collected is analyzed through various methods designed to differentiate sections of track including Gaussian Mixture Model sorting algorithms, inspection via Short Time Fourier Transforms, Discrete Wavelet Transforms, and manual inspection. None of the methods can be done automatically; they each require a different amount of setup and pre-processing before the raw data can be made suitable for the analysis offered by each. The pre-processing can account for dropped data and can be used to identify some false positives such as switches or lubricators. The test results indicate that the system provides a distinctly different measurement in the sections that are doctored to have less track stability than the section with nominally sufficient stiffness. The detection of the loose track in the tangent sections, however, proves to be less reliable. For those, a mostly ad hoc approach is necessary to match the measured data with video images to pinpoint the exact location of the measurements. It is not clear to what extent such approaches would be feasible in practice. Further evaluations of the test data may be used to shed more light on practical analysis methods—possibly wavelets—that are more automated and less ad hoc. They can also provide alternative system setups or designs of experiments for future tests at TTC or on revenue service tracks. / Master of Science / The purpose of this study is to evaluate the effectiveness of a set of Doppler Lidar sensors for their ability to determine the locations of weaker sections of railroad track. These weaker sections could cause damage to the track or passing trains by deforming or buckling under load. A set of tests are performed at the Transportation Technology Center's High Tonnage Loop to evaluate these capabilities. The track had two sections, one of curved track the other of straight track, where the rail was purposefully weakened by removing retaining spikes from the railroad ties. The weakened sections were created by removing the vertical retaining spikes in eight consecutive ties. The tests were conducted at speeds of between 10 to 40 mph, and the sensors measured both the vertical and lateral movement of both rails. The results of these measurements were compared with the unaffected rail. The collected data is analyzed using various data processing techniques. These techniques included using a sorting algorithm to find sections of track with different characteristics as well as inspecting the time and frequency content of the data. None of these methods are automated, and each requires specific setup and adjustment to be effective. The data also needs to be prepared by correcting for any missing or incorrect data points. The tests indicate that the system is able to differentiate between the purposefully weakened track and the rest of the track, however the clearest results of this were for the weakened track in the curve. The straight track results were able to be found with the addition of aligning the video, Lidar, and GPS data sets. It is not clear whether the system could be improved to detect this type of weakness in straight track in practice. Additional testing and evaluation could serve to expand the range of data analysis methods used in differentiating the track conditions and could serve to automate the process. Additionally, alternative test setups could provide further information as to the capabilities of the sensors to detect different types of weakened track.

Several different aspects of floor vibrations were studied during this research. The focus of the research was on developing a computer modeling technique that will predict the fundamental frequency of vibration and the peak acceleration due to walking excitation as given in AISC Design Guide 11, Floor Vibrations Due to Human Activity (Murray, et al., 1997). For this research several test floors were constructed and tested, and this data was supplemented with test data from actual floors. A verification of the modeling techniques is presented first. Using classical results, an example from the Design Guide and the results of some previous research, the modeling techniques are shown to accurately predict the necessary results. Next the techniques were used on a series of floors and the results were compared to measured data and the predictions of the current design standard. Finally, conclusions are drawn concerning the success of the finite element modeling techniques, and recommendations for future research are discussed. In general, the finite element modeling techniques can reliably predict the fundamental frequency of a floor, but are unable to accurately predict the acceleration response of the floor to a given dynamic load. / Master of Science

The constituent parts of a magnetorheological (MR) sandwich beam combine to create a powerful damping device. The apparent viscosity of an MR fluid can change with the application of an adjacent magnetic field. Typically, this apparent viscosity rises as the field gets stronger. The resulting resistance to motion makes MR fluids a great choice for damping applications. The sandwich beam is a composite structure with two elastic outer layers and a damping material in between that forms the core layer. Using MR fluid as the damping agent produces good and tunable damping performance while possessing the benefits of a sandwich beam, such as its ease of construction and its form factor. This dissertation pursues two goals. The first goal is related to modeling a beam's dynamics. In addition to creating a new beam model, this research tests the limitations of the DiTaranto model, a popular model in the literature. The second goal is to apply time-varying magnetic fields to the beam to balance damping performance and electromagnet power consumption when the beam undergoes free-decay vibration. The model findings showed that while the DiTaranto model works better than the proposed models, this beam model tends to work best for stiffer outer layers and for electromagnets (assuming they do not span the beam's entire length) placed at the beam's middle or free end, while softer outer layers lead to improved damping performance. With respect to the free-decay analysis, time-varying magnetic fields can possess comparable or faster decay when compared to a constant magnetic field; turning the field on or off during free decay leads to slightly decreased damping performance but with less power consumption for stiffer beams, while softer beams can enjoy both reduced consumption and increased damping when using a damping method like synchronous switch damping.

Résumé : Ce projet de recherche est composé de trois parties principales : la première comprend l'analyse expérimentale et la simulation des performances vibratoires de matériaux avec amortissement viscoélastique, en tant que traitements acoustiques appliqués aux structures du fuselage d'un avion. La deuxième partie comprend l'analyse expérimentale et le calcul de la performance acoustique de ces matériaux amortissant en comparaison avec l'effet d'une masse équivalente. Enfin, la troisième partie est une étude paramétrique sur les effets de localisation, de la densité et de la taille d'un traitement massique. Les systèmes d'isolation phoniques typiquement employés dans la construction des fuselages d'avions sont composés de matériaux poreux, avec ou sans des matériaux amortissant (matériaux viscoélastiques). La performance et donc l'utilité de ces traitements amortissant, en comparaison avec une couche de masse équivalente, reste une question largement ouverte. Dans ce travail on a comparé numériquement et expérimentalement les performances acoustiques d'un traitement amortissant avec celui d'une masse équivalente tous les deux incorporées dans le traitement phonique et ceci pour plusieurs types d'excitations. Deux structures représentant des fuselages, une en aluminium et la seconde en carbone composite, ont été sélectionnées pour cette étude ainsi que deux matériaux poreux couramment utilisés en aéronautique : une laine en fibre de verre et une mousse à cellules ouvertes. Deux types d'excitations ont été étudiés numériquement et expérimentalement. La première est une excitation acoustique (champ diffus) et la seconde mécanique (forces ponctuelles). Une troisième, excitation par couche limite turbulente a été étudié numériquement. Dans tous les cas, la perte par insertion du traitement acoustique est utilisée comme indicateur principal de la performance. D'autres indicateurs comme le coefficient d'absorption, le coefficient de perte par amortissement et la vitesse quadratique moyenne sont aussi utilisés pour mieux cerner et expliquer l'effet du traitement. Il a été démontré que l'utilisation d'une couche de masse équivalente à un traitement viscoélastique conduit systématiquement à la meilleure performance acoustique et ceci pour les trois types d'excitations étudiées. En particulier, dans le cas classique où le traitement amortissant est appliqué directement au fuselage. Dans ce dernier cas, les effets de doubles parois créés par la couche massique, positionnée judicieusement loin du fuselage, augmentent la performance en moyennes et hautes fréquences. Les performances en basses fréquences restent limitées par la fréquence de résonance double parois. Et même l'effet amortissant des traitements viscoélastiques, théoriquement visible aux résonances et coïncidences du système, se trouve limité par l'amortissement ajouté par le montage et le traitement absorbants. Cependant, l'efficacité de la couche massique est compromise par les difficultés d'installations et en particulier pour les fibreux. Les résultats de cette thèse restent toutefois limités par notre choix de structures et de traitements étudiés. / Abstract : The project is made up of three main parts. The first part involves a comprehensive experimental and numerical analysis of viscoelastic damping materials as acoustic treatments to aircraft fuselage structures. The second part involves numerical and experimental acoustic comparison of viscoelastic damping material to equivalent mass. And the third part is a parametric study of equivalent mass for the effects of mass location, density and size. The goal of the project is to identify the vibroacoustic effect of viscoelastic material damping of fuselage skin, and develop possible alternatives to damping. The insulation systems (typically used on aircraft) that are made up of porous materials with or without viscoelastic damping material or equivalent mass were called sound packages throughout this document. The viscoelastic damping material and equivalent mass both incorporated in sound packages were acoustically compared. Fiberglass and open cell foam were used as porous materials. The viscoelastic damping material used in this study is constraining layer damping and abbreviated as CLD. The equivalent mass was an impervious screen. Both representative Aluminum and carbon composite fuselage skin structures were treated with sound packages as part of the comparison. The vibroacoustic performance indicators were used to characterize the sound packages. The indicators were airborne insertion loss (ABIL), structure borne insertion loss (SBIL), turbulent boundary layer insertion loss (TBLIL), average quadratic velocity (AQV), damping loss factor (DLF), absorption coefficient, and radiation efficiency. Diffuse field acoustic excitation was used to obtain the vibroacoustic indicators of ABIL and absorption coefficient. Mechanical excitation was used to obtain SBIL, AQV, DLF, absorption coefficient, and radiation efficiency. Turbulent boundary layer excitation was modeled to obtain TBLIL. The numerical methods of finite element method (FEM) and transfer matrix method (TMM) were used to calculate all of the above vibroacoustic performance indicators. Experimentally, ABIL, SBIL, AQV, DLF and radiation efficiency were measured. Experimental modal analysis was also performed to characterize representative Aluminum and carbon composite fuselage skin structures. Based on the numerical analysis, equivalent mass generated a double or multiple (in case of double wall layer configuration) wall effect and hence became an effective acoustic insulator as part of sound packages at mid to high frequencies. Even at coincidence frequencies (in case of the representative carbon composite fuselage skin), the equivalent mass layer was more effective than viscoelastic damping material. However, the drawback was the occurrence of the double wall resonance at lower frequencies which compromised the effectiveness. Nevertheless, the parametric study of equivalent mass revealed that equivalent mass is superior to viscoelastic damping material at reduced weight in term of vibroacoustic performance indicators of overall ABIL/SBIL/TBLIL in the frequency range of 100 to 6300 Hz and mean ABIL/SBIL/TBLIL in SIL (octave lk, 2k, 4k Hz) frequency range.

Parmi les méthodes appliquées dans le cadre de la maintenance des installations industrielles, l'analyse vibratoire constitue une des plus répandues. En effet, les signatures vibratoires apparaissant sur une installation en cours de fonctionnement sont étroitement liées à leur comportement dynamique et à leur état fonctionnel. Ce travail a pour objectif de développer et expérimenter des techniques et outils de calculs numériques pour l'interprétation d'indicateurs d'état issus de mesures vibratoires sur une machine tournante. La validation est faite sur un ensemble motoréducteur à engrenages. Pour cela, nous avons développé deux outils d'analyse numérique : un premier permettant de déterminer les caractéristiques modales d'une structure complexe puis un second, développé sur la base des ondelettes, pour détecter les défauts naissants sur un motoréducteur. Les performances relatives des différents outils sont comparées au regard de ce qui se fait dans la littérature. Enfin, une étude expérimentale sur banc d'essais a été menée dans le but de tester la sensibilité et les limites de la méthode. Le mémoire est articulé comme suit : une première partie développe les principales techniques vibratoires actuelles avec leurs performances et limites. De la deuxième partie traitant les théories et méthodes d'analyse modale découle une troisième présentant des méthodes améliorées. Dans la quatrième partie, une étude expérimentale sur banc d'essais a été menée dans le but de tester la sensibilité de la méthode. Une approche par la décomposition en ondelettes des signaux a été notamment utilisée. Il est démontré que cette méthode a une application intéressante dans le domaine des analyses vibratoires de structures complexes / Vibrations analysis appears to be one of the most efficient methods among those that are actually used in the field of preventive and condition-based maintenance of industrial equipments. Indeed, vibration signs from a working machine depend tightly on its dynamical behaviour and health. This thesis consists on developing some new techniques and numerical calculation tools which help while interpreting indicators issued from vibrations measurements of rotating machinery. Validation has been done especially on case study of a complex bench constituted by motor with gear transmission. Technically, it aims on one part in determining modal characteristics of the whole system, and on another part in finding out a reliable method for rotating machinery defaults detecting. The first part resumes main present vibrating techniques. From the second part which treats theoretical modal analysis arises a developing improved methods third one. At this step, some numerical codes permitting treatment and quick interpretation of analysis results were drawn up. On the fourth part, an experimental study on a test bed was carried out with the aim of confronting theoretical, analytical and numerical results with real ones.An approach by wavelet decomposition of signals was particularly used here. It is shown that this method has got interesting application in the field of complex structures vibration analysis