This work addresses issues in energy harvesting that have plagued the potential use of harvesting through the piezoelectric effect at the MEMS scale. Effective energy harvesting devices typically consist of a cantilever beam substrate coated with a thin layer of piezoceramic material and fixed with a tip mass tuned to resonant at the dominant frequency of the ambient vibration. The fundamental natural frequency of a beam increases as its length decreases, so that at the MEMS scale the resonance condition occurs orders of magnitude higher than ambient vibration frequencies rendering the harvester ineffective. Here we study two new geometries for MEMS scale cantilever harvesters. The zigzag and spiral geometries have low fundamental frequencies which can be tuned to the ambient vibrations. The second issue in energy harvesting is the frequency sensitivity of the linear vibration harvesters. A nonlinear hybrid energy harvester is presented that has a wide frequency bandwidth and large power output. Finally, linear and nonlinear energy harvesting devices are designed for powering the cardiovascular pacemakers using the vibrations in the chest area induced by the heartbeats. The mechanical and electromechanical vibrations of the zigzag structure are analytically modeled, verified with Rayleigh's method, and validated with experiments. An analytical model of coupled bending torsional vibrations of spiral structure is presented. A novel approximation method is developed for analyzing the electromechanical vibrations of energy harvesting devices. The unified approximation method is effective for linear, nonlinear mono-stable, and nonlinear bi-stable energy harvesting. It can also be utilized for piezoelectric, electromagnetic or hybrid energy harvesters. The approximation method accurately approximates the effect of energy harvesting on vibrations of energy harvester with changes in damping ratio and excitation frequency. Experimental investigations are performed to verify the analytical model of the nonlinear hybrid energy harvester. A detailed experimental parametric study of the nonlinear hybrid design is also performed. Linear and nonlinear energy harvesting devices have been designed that can generate sufficient amounts of power from the heartbeat induced vibrations. The nonlinear devices are effective over a wide range of heart rate. / Ph. D.

The possibility of using a commercially available structural analysis program to predict the response of a floor system due to walking excitation as given in AISC Design Guide 11, Floor Vibrations Due to Human Activity (Murray, et al., 1997) was explored. This research included ideal floors that did not have measured values as well as several case study floors that do have measured values for the fundamental frequency. First, multiple model set-ups and loading protocols are applied to the ideal floors and the results compared to results from the Design Guide procedure. A recommendation of the best combination of a model set-up and loading protocol that best matches the Design Guide procedure results is made. Then, case study floors are modeled with the recommended model set-up and loading protocol, and the results compared to the results from the Design Guide procedure and to measured fundamental frequencies. The peak accelerations are also compared to subjective evaluations as to the acceptability of the system. Next, multiple systems were analyzed using five different modeling techniques, including the Design Guide Method, an alteration of the Design Guide Method, the Rayleigh Method, the Analytical Method, and the structural analysis program method, in an attempt to determine the source of discrepancies between the structural analysis program method and the Design Guide method. Finally, conclusions are drawn regarding the structural analysis program procedure as well as possible sources of differences. In general, the structural analysis program procedure reliably predicts the fundamental frequency of a floor system, but does not predict the Design Guide peak acceleration under dynamic loading. The difference in the effective mass of a system between the two methods is a source of discrepancy. / Master of Science

Experimental and analytical research was conducted to address the vibration properties of Long Span Deck Floor Systems (LSDFS). The research comprised three stages. In the first part, experimental in-situ tests were conducted on thirteen bays of buildings under construction. The natural frequencies and acceleration responses were captured to observe the vibration behavior of the tested floors. In the second part, a laboratory footbridge was constructed to determine the fixity level attained at the supports when a LSDFS is supported by CMU walls. For this purpose, the footbridge was tested with three support conditions, and a number of experiments were carried out to determine the dynamic properties of the structure. Static tests using both point and distributed loadings were conducted to measure the deflections at the footbridge midspan. The static test results were compared to the theoretical deflections for a pinned-end beam and a fixed-end beam. Dynamic tests using experimental modal analysis techniques were conducted to determine the natural frequencies and mode shapes of the structure. The measured fundamental natural frequency of the footbridge was compared to the frequencies calculated for a simply supported beam and a beam with fixed ends, to determine the degree of fixity attained in the connection between the LSDFS and the supporting walls. In the last part of the research, three analytical procedures to predict modal characteristics of long span deck floor systems are studied. Floor frequencies are calculated using finite element analyses. Two design guides for floor vibration analysis were used to calculate natural frequencies and response accelerations. The predicted results obtained from the analytical methods are compared to the experimental results to determine their accuracy. Recommendations for the use of the analytical methods are provided. / Master of Science

A control algorithm is developed and applied to a previously designed tunable vibration absorber. The adaptive vibration absorber is capable of detecting the frequency of the driving force and tuning itself automatically to that particular frequency. The primary structure was previously designed to obtain a certain natural frequency. The absorber structure was previously designed so that its range of frequencies includes the natural frequency of the primary structure. The primary structure design consists of a cantilever beam with the absorber attachment hardware, and the vibration absorber assembly consists of three rods and a stepper motor. The control algorithm uses a look-up table and a gradient search to optimize the effectiveness of the absorber for vibration reduction on the primary structure. The look-up table uses an equation, based on experimental data, to transform a given voltage input, directly proportional to the forcing frequency, into an output command necessary to adjust the natural frequency of the absorber. Once the input voltage reaches a steady state, the gradient search routine adjusts the natural frequency of the absorber to ensure the absorber is tuned to the optimal frequency that minimizes the primary structure vibration. The primary structure with the adaptive absorber offers significant reduction to the vibration amplitudes of the primary structure, as compared to both the primary structure with no absorber and the primary structure with a passive absorber, throughout the 45 Hz to 71 Hz and 73 Hz to 108 Hz range. The primary structure with no absorber has a 1^st mode natural frequency of 72 Hz and offers the lowest vibration amplitudes, as compared to both the primary structure with the adaptive absorber and the primary structure with a passive absorber, throughout the ranges of 30 Hz to 45 Hz and 108 Hz to 130 Hz. The primary structure with the passive absorber offers the lowest vibration amplitudes of the primary structure, as compared to both the primary structure with no absorber and the primary structure with the adaptive absorber, throughout the 71 Hz to 73 Hz range. / Master of Science

The work is focused in investigating the effectiveness of discretized damping tapes applied to a cantilever beam subjected to free and forced vibrations. The work is divided into three main sections. First, we performed material characterization of the viscoelastic (VE) pressure sensitive adhesive layer of the damping tapes. To do so, we designed a novel quad shear specimen to measure shear storage and loss moduli, and tan delta from dynamic mechanical analyzer measurements. Second, the optimal discretization length for different damping tapes was experimentally determined and analytically verified using linear viscoelasticity and basic strength of materials and vibrations principles. These results showed a mean to improve the damping of a structure without increasing the weight of the added damping layer. Third, a nonlinear analysis was performed for cantilever beams with damping layers subjected to parametric excitation. Comparison of the response amplitude of the parametrically excited beam was performed for different discretization lengths, and system identification of the nonlinear parameters was carried out. The effects of large deflections of a beam under parametric excitation were analyzed; large deflections were found to induce localized buckling of the stiff constraining layer of the damping tape that would invalidate some of the assumptions and analytical solutions that do not take such phenomena into account. / Master of Science

Vibrations resulting from earthquakes, machinery, or unanticipated shocks may be very damaging and costly to structures. To avoid such damage, designers need a structural system that can dissipate the energy caused by these vibrations. Using elastically buckled struts may be a viable means to reduce the harmful effects of unexpected vibrations. Post-buckled struts can support high axial loads and also act as springs in a passive vibration isolation system by absorbing or dissipating the energy caused by external excitation. When a base excitation is applied, the buckled strut may act to reduce the dynamic force transmitted to the system, thus reducing the structural damage to the system. Several models of buckled and pre-bent struts are examined with different combinations of parameters and end conditions. The models include pinned or fixed columns supporting loads above their buckling load, and columns with an initial curvature supporting various loads. The varying parameters include external damping, internal damping, and stiffness. The columns will be subjected to simple harmonic motion applied at the base or to a multi-frequency base excitation. The response of each model is measured by the deflection transmissibility of the supported load over a large range of frequencies. Effective models reduce the motion of the supported load over a large range of frequencies. / Master of Science

A wide range of physical systems are modeled as axially moving strings; such examples are belts, tapes, wires and fibers with applied electromagnetic fields. In this study, we propose a model that describes the motion of a current-carrying conductive string in a lateral magnetic field, while it is being pulled axially. This model is a generalization of past studies that have neglected one or more properties featured in our system. It is assumed that the string is moving with a constant velocity between two rings that are a finite distance apart. Directions of the magnetic field and the motion of the string coincide. The problem is first considered in a static setting. Stability critical values of the magnetic field, pulling speed, and current are shown to exist when the uniform motion (along a string line) of the string buckles into spiral forms. In the dynamic setting, conditions for stability of certain solutions are presented and discussed. It is shown that there is a divergence between the critical values in the linear dynamic and static cases. Furthermore, traveling wave solutions are examined for certain cases of our general system. We develop an approximate solution for a nonlinear moving string when a periodic nonstationary current flows through the string. Domains of parameters are defined when the string falls into a pre-chaotic state, i.e., the frequency of vibrations is doubled. / MS / The modeling and analysis of elastic conductors has applications in areas ranging from manufacturing to particle physics. In this study, we model the motion of a conductive string being pulled (between two rings) while a magnetic field is applied in the lateral direction. This system’s stability is categorized through certain parameters such as the applied magnetic field, speed of pulling, and current flowing through the string. The equilibrium states are also analyzed. When the string has a periodic current, approximate solutions (string shape/orientation) are computed. In this case, we find domains of parameters that give rise to chaos. Wave speeds of traveling wave solutions are also found for certain cases.

The transmission line is an underappreciated style of loudspeaker enclosure characterized by an acoustic labyrinth stemming from the rear of the speaker driver. In practice, the transmission line enclosure produces airy sound uncharacteristic of other styles, at the cost of more pronounced resonant peaks. The most important practical drawback of this loudspeaker enclosure design is the difficulty of properly applying damping to these enclosures. Ideally, this difficulty can be mitigated using an analytical model that accurately predicts the SPL frequency response of a transmission line loudspeaker system for a given geometry and mass of damping material. This research takes the first step towards establishing such a model by developing a limited model for a simple enclosure geometry. Through the application of a modal analysis, this research predicts the frequency response of the enclosure for the first five modes, discusses the effect damping has on this response, and experimentally verifies the produced outputs. For the simplified transmission line enclosure, the developed model successfully predicts the target portion of the frequency response. The model produces accurate results for a range of damping levels using experimentally derived damping ratios for the first five modes. The resulting curves for each modal damping ratio allow for a set of novel damping ratios to be produced from an input mass of damping material. Through this process, an input mass of damping material produces the predicted frequency response for a straight, non-tapered transmission line enclosure. This prediction can make damping a transmission line enclosure much more efficient, allowing for transmission line loudspeakers to be more widely available.

La mesure des vibrations de la roue d'une turbine hydraulique en opération demeure encore aujourd'hui un dé, particulièrement à l'échelle modèle. L'installation d'appareils de mesure(jauges de contrainte et accéléromètres) sur la roue en rotation a un effet non négligeable sur l 'écoulement du fluide et affecte le comportement structural de la roue (masse ajoutée). Face à ce problème, l'utilisation d'appareils de mesure sans contact localisés sur le repère fixe est une solution intéressante pour mesurer les vibrations d'une structure en rotation. Ce mémoire de maîtrise présente une étude sur l'utilisation de sondes à courant de Foucault localisées sur le repère fixe pour mesurer les vibrations au niveau de la ceinture d'une roue de type Francis en opération. D'abord, une méthode de mesure est développée an d'éliminer le dédoublement des résonances présent dans la réponse en fréquence des mesures de vibrations d'une structure en rotation prises à partir du repère xe. Une validation numérique de cette méthode démontre qu'il est possible de réaliser l'analyse modale de la structure en rotation. Par la suite, un montage expérimental est conçu pour mesurer les vibrations d'un anneau en rotation et immergé sous l'eau an d'appliquer la méthode proposée. Finalement, une campagne de mesures préliminaires est réalisée avec le montage expérimental an de tester les sondes à courant de Foucault pour mesurer les vibrations dans des conditions opératoires similaires à celles retrouvées dans les turbines hydrauliques. Ces mesures préliminaires permettent également d'observer le comportement du montage conçu sur les mesures vibratoires de l'anneau. / The vibrations measurement of hydraulic turbine runners in operation is still actually a challenge, especially at the model scale. It is possible to x sensors on the rotating part likes train gauges and accelerometers, but these sensors have a significant effect on the structural behavior of the runner (added mass) and on the hydraulic ow. To deal with this issue, the usage of a non-contact measuring devices located on the non-rotating frame is an interesting solution to measure the vibrations of a rotating structure. This Master's thesis presents the study of the use of eddy current sensors located on the fixed frame to measure the vibrations of an operating Francis runner's band. First, a measurement method is developed to eliminate the duplication of resonances in the frequency response of the vibration measurements of a rotating structure taken from the non-rotating frame. A numerical simulation of this method shows that it is possible to perform the modal analysis of the rotating structure. Subsequently,an experimental bench test is designed to measure the vibrations of a submerged rotating ring in order to apply the proposed method. Finally, a set of preliminary measurements is achieved with the experimental bench to test the eddy current sensors to measure the vibrations under similar operating conditions that can be found in the hydraulic turbines. These preliminary measurements allow us to observe the behavior of the bench test on the vibration measurements of the ring.

Cette étude de la compaction d’un empilement granulaire par vibrations horizontales a été réalisée dans le cadre d’un partenariat avec le groupe MERSEN pour une application au sable contenu dans ses fusibles. L’objectif scientifique est de développer la compréhension des mécanismes mis en jeu dans un milieu granulaire vibré horizontalement. Deux approches ont été utilisées en parallèle, l’une expérimentale, l’autre par simulation numérique. L’approche expérimentale a été réalisée sur des grains de silice de diamètre moyen 500 m. Un récipient de quelques centimètres est soumis à un mouvement sinusoïdal de fréquence comprise entre 20 et 200 Hz avec des accélérations allant jusqu’à 10 g. Le dispositif instrumenté permet la mesure instantanée de la force et de l’accélération, la vitesse des grains aux parois (PIV) ainsi que la densité globale du milieu. L’approche numérique est basée sur la méthode des éléments discrets (DEM). Des méthodes spécifiques d’analyse des résultats ont été développées pour assurer la comparaison avec l’expérience. Elles permettent d’obtenir des informations qui ne sont pas accessibles expérimentalement comme les densités, vitesses et contraintes locales dans l’ensemble de l’empilement. Dans le cas d’un récipient ouvert, la simulation permet de retrouver les résultats expérimentaux : rouleaux de convections, seuils de comportement, influence de l’accélération… Des résultats originaux ont été établis dans les expériences et les simulations comme une croissance de la vitesse des grains avec la longueur du récipient. La simulation a aussi permis d’obtenir des résultats spécifiques comme l’influence du coefficient de friction sur le sens des rouleaux et la caractérisation des contraintes au sein de l’empilement. L’écoulement des grains à travers des orifices circulaires de différentes dimensions a été également étudié. Le comportement du sable dans un récipient fermé (milieu confiné) a été étudié au cours d’un remplissage progressif. Des différences significatives ont été constatées lorsque le taux de remplissage devient élevé. Des mesures d’accélération et de force sur l’ensemble du dispositif ont permis de définir et de mesurer une masse apparente et l’énergie dissipée par le dispositif. Des modèles descriptifs ont permis de comprendre les comportements observés. Ces résultats sont à l’origine d’un brevet déposé par le groupe MERSEN sur le contrôle du remplissage. / This work on the densification of a granular medium under horizontal vibrations was realised in the context of an industrial study on sand in fuses, undertaken by the firm MERSEN. The scientific purpose is the understanding of the mechanisms involved in horizontally vibrated granular media. Both experiments and computer simulations were used. Experiments were conducted with 500 µm silica grains. Sinusoidal accelerations up to 10 g were applied to a container of a few centimetres using frequencies between 20 and 200 Hz. The experimental device enables instantaneous force, acceleration, grain velocity on the walls (PIV) and mean bulk density to be measured. Discrete element method (DEM) was used for the computer simulations. Specific techniques were developed to analyse the results and compare them with experiments. Computer simulations provided data which are not experimentally available such as local values of density, velocities and stress inside the particle packing. In the case of an open container, simulation results are in good agreement with experimental ones (convection rolls, thresholds, effect of acceleration...). Original results are obtained in both experiments and simulations, such as a grain velocity increase with the container length. Simulation provided specific results such as the effect of friction coefficients on the direction of rotation of convection rolls and the characterization of stress inside the particle packing. The flowability of grains across circular holes of various sizes was also studied. The behaviour of sand in a closed container (confined medium) was studied during a progressive filling. Significant differences were observed when the filling rate becomes high. The dissipated energy and the apparent mass of the vibrated device were defined and measured using acceleration and force measurements. Specific models were built to analyse and understand the observed behaviour. Some results on the filling control were patented by MERSEN.