Dynamic problems in footbridges, such as sensible vibrations caused by human induced loading, has on a number of occasions been observed. These vibrations are rarely an ultimate limit state problem, but can be perceived as unpleasant by the pedestrian. In design guidelines there are propositions for how to asses the dynamic problem. However, they only take the walking load into account. It has been shown that, in the case of a running load, accelerations that lie above the comfort zone can occur and that running loads are more severe than walking loads in some cases. It is possible that the running load case has to be considered in future guidelines, and finding a feasible design methodology demands a lot of work. In this thesis, a method aimed to be easily used by a designer is analyzed. The amplitude of acceleration received as a result from a dynamic analysis in a commercial FEM software, was reduced by reduction factors to generate accelerations closer to reality. This could be identified and verified against recommendations.

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Piezoelectric-based energy harvesting devices provide an attractive approach to powering remote devices as ambient mechanical energy from vibrations is converted to electrical energy. These devices have numerous potential applications, including actuation, sensing, structural health monitoring, and vibration control -- the latter of which is of particular interest here. This work seeks to develop an understanding of energy harvesting behavior within the framework of a semi-active technique for reducing turbomachinery blade vibrations, namely resonance frequency detuning. In contrast with the bulk of energy harvesting research, this effort is not focused on maximizing the power output of the system, but rather providing the low power levels required by resonance frequency detuning. The demands of this technique dictate that harvesting conditions will be far from optimal, requiring that many common assumptions in conventional energy harvesting research be relaxed. Resonance frequency detuning has been proposed as a result of recent advances in turbomachinery blade design that have, while improving their overall efficiency, led to significantly reduced damping and thus large vibratory stresses. This technique uses piezoelectric materials to control the stiffness, and thus resonance frequency, of a blade as the excitation frequency sweeps through resonance. By detuning a structure*s resonance frequency from that of the excitation, the overall peak response can be reduced, delaying high cycle fatigue and extending the lifetime of a blade. Additional benefits include reduced weight, drag, and noise levels as reduced vibratory stresses allow for increasingly light blade construction. As resonance frequency detuning is most effective when the stiffness states are well separated, it is necessary to harvested at nominally open- and short-circuit states, corresponding to the largest separation in stiffness states. This presents a problem from a harvesting standpoint however, as open- and short-circuit correspond to zero charge displacement and zero voltage, respectively, and thus there is no energy flow. It is, then, desirable to operate as near these conditions as possible while still harvesting sufficient energy to provide the power for state-switching. In this research a metric is developed to study the relationship between harvested power and structural stiffness, and a key result is that appreciable energy can be harvested far from the usual optimal conditions in a typical energy harvesting approach. Indeed, sufficient energy is available to power the on-blade control while essentially maintaining the desired stiffness states for detuning. Furthermore, it is shown that the optimal switch in the control law for resonance frequency detuning may be triggered by a threshold harvested power, requiring minimal on-blade processing. This is an attractive idea for implementing a vibration control system on-blade, as size limitations encourage removing the need for additional sensing and signal processing hardware.

In this study, Ritz method has been employed to analyze the following problems: free vibrations of plates with curvilinear stiffeners, the lowest 100 frequencies of thick isotropic plates, free vibrations of thick quadrilateral laminates and free vibrations and static deformations of rectangular laminates, and sandwich structures. Admissible functions in the Ritz method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made possible by additive manufacturing, both plate and stiffeners are modeled using a first-order shear deformation theory. For the thick isotropic plates and laminates, a third-order shear and normal deformation theory is used. The accuracy and computational efficiency of formulations are shown through a range of numerical examples involving different boundary conditions and plate thicknesses. The above formulations assume the whole plate as an equivalent single layer. When the material properties of individual layers are close to each other or thickness of the plate is small compared to other dimensions, the equivalent single layer plate (ESL) theories provide accurate solutions for vibrations and static deformations of multilayered structures. If, however, sufficiently large differences in material properties of individual layers such as those in sandwich structure that consists of stiff outer face sheets (e.g., carbon fiber-reinforced epoxy composite) and soft core (e.g., foam) exist, multilayered structures may exhibit complex kinematic behaviors. Hence, in such case, C_z⁰ conditions, namely, piecewise continuity of displacements and the interlaminar continuity of transverse stresses must be taken into account. Here, Ritz formulations are extended for ESL and layerwise (LW) Nth-order shear and normal deformation theories to model sandwich structures with various face-to-core stiffness ratios. In the LW theory, the C⁰ continuity of displacements is satisfied. However, the continuity of transverse stresses is not satisfied in both ESL and LW theories leading to inaccurate transverse stresses. This shortcoming is remedied by using a one-step well-known stress recovery scheme (SRS). Furthermore, analytical solutions of three-dimensional linear elasticity theory for vibrations and static deformations of simply supported sandwich plates are developed and used to investigate the limitations and applicability of ESL and LW plate theories for various face-to-core stiffness ratios. In addition to natural frequency results obtained from ESL and LW theories, the solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial finite element method (FEM) software, ABAQUS, are provided. It is found that LW and ESL (even though its higher-order) theories can produce accurate natural frequency results compared to FEM with a considerably lesser number of degrees of freedom. / Doctor of Philosophy / In everyday life, plate-like structures find applications such as boards displaying advertisements, signs on shops and panels on automobiles. These structures are typically nailed, welded, or glued to supports at one or more edges. When subjected to disturbances such as wind gusts, plate-like structures vibrate. The frequency (number of cycles per second) of a structure in the absence of an applied external load is called its natural frequency that depends upon plate's geometric dimensions, its material and how it is supported at the edges. If the frequency of an applied disturbance matches one of the natural frequencies of the plate, then it will vibrate violently. To avoid such situations in structural designs, it is important to know the natural frequencies of a plate under different support conditions. One would also expect the plate to be able to support the designed structural load without breaking; hence knowledge of plate's deformations and stresses developed in it is equally important. These require mathematical models that adequately characterize their static and dynamic behavior. Most mathematical models are based on plate theories. Although plates are three-dimensional (3D) objects, their thickness is small as compared to the in-plane dimensions. Thus, they are analyzed as 2D objects using assumptions on the displacement fields and using quantities averaged over the plate thickness. These provide many plate theories, each with its own computational efficiency and fidelity (the degree to which it reproduces behavior of the 3-D object). Hence, a plate theory can be developed to provide accurately a quantity of interest. Some issues are more challenging for low-fidelity plate theories than others. For example, the greater the plate thickness, the higher the fidelity of plate theories required for obtaining accurate natural frequencies and deformations. Another challenging issue arises when a sandwich structure consists of strong face-sheets (e.g., made of carbon fiber-reinforced epoxy composite) and a soft core (e.g., made of foam) embedded between them. Sandwich structures exhibit more complex behavior than monolithic plates. Thus, many widely used plate theories may not provide accurate results for them. Here, we have used different plate theories to solve problems including those for sandwich structures. The governing equations of the plate theories are solved numerically (i.e., they are approximately satisfied) using the Ritz method named after Walter Ritz and weighted Jacobi polynomials. It is shown that these provide accurate solutions and the corresponding numerical algorithms are computationally more economical than the commonly used finite element method. To evaluate the accuracy of a plate theory, we have analytically solved (i.e., the governing equations are satisfied at every point in the problem domain) equations of the 3D theory of linear elasticity. The results presented in this research should help structural designers.

Converting vibrations to a usable form of energy has been the topic of many recent investigations. The ultimate goal is to convert ambient or aeroelastic vibrations to operate low-power consumption devices, such as microelectromechanical systems, heath monitoring sensors, wireless sensors or replacing small batteries that have a nite life span or would require hard and expensive maintenance. The transduction mechanisms used for transforming vibrations to electric power include: electromagnetic, electrostatic, and piezoelectric mechanisms. Because it can be used to harvest energy over a wide range of frequencies and because of its ease of application, the piezoelectric option has attracted significant interest. In this work, we investigate the performance of different types of piezoelectric energy harvesters. The objective is to design and enhance the performance of these harvesters. To this end, distributed-parameter and phenomenological models of these harvesters are developed. Global analysis of these models is then performed using modern methods of nonlinear dynamics. In the first part of this Dissertation, global nonlinear distributed-parameter models for piezoelectric energy harvesters under direct and parametric excitations are developed. The method of multiple scales is then used to derive nonlinear forms of the governing equations and associated boundary conditions, which are used to evaluate their performance and determine the effects of the nonlinear piezoelectric coefficients on their behavior in terms of softening or hardening. In the second part, we assess the influence of the linear and nonlinear parameters on the dynamic behavior of a wing-based piezoaeroelastic energy harvester. The system is composed of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. Linear analysis is performed to determine the effects of the linear spring coefficients and electrical load resistance on the flutter speed. Then, the normal form of the Hopf bifurcation (flutter) is derived to characterize the type of instability and determine the effects of the aerodynamic nonlinearities and the nonlinear coefficients of the springs on the system's stability near the bifurcation. This is useful to characterize the effects of different parameters on the system's output and ensure that subcritical or "catastrophic" bifurcation does not take place. Both linear and nonlinear analyses are then used to design and enhance the performance of these harvesters. In the last part, the concept of energy harvesting from vortex-induced vibrations of a circular cylinder is investigated. The power levels that can be generated from these vibrations and the variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion and generated voltage is presented. Linear analysis of the electromechanical model is performed to determine the effects of the electrical load resistance on the natural frequency of the rigid cylinder and the onset of the synchronization region. The impacts of the nonlinearities on the cylinder's response and energy harvesting are then investigated. / Ph. D.

In this thesis we use a new numerical code, based upon a mixed FEM-Runge-Kutta method, for the analysis and the design of plane 2-dimensional smart structures. We applied the developed code to the study of arbitrarily shaped piezo-electromechanical (PEM) plates. This code is based on a weak formulation of their governing equations as found in [18]. The optimal parameters needed to synthesize the appropriate electric networks are computed, and the overall performances of such plates are investigated. In particular, two examples are studied: firstly, a simple case is used to test the main features of the code; secondly, a more complex PEM plate is designed and analyzed by means of the proposed numerical approach. / Master of Science

<p> Two phase flow induced vibrations is a field that has many inherent modelling difficulties, making research in the area challenging. In order to study the problem more closely, a two phase flow loop using Freon 11 had been designed and commissioned at McMaster University. The initial design required some modifications to make the loop as "user friendly" as possible. The final result meets this desired capability. </p> <p> The loop was designed so that research into vibrations in tube bundles could be carried out. A test section had been designed to facilitate this task. However, this design also required modifications. Additionally, new vibration monitoring instrumentation making use of light was developed to avoid the detrimental effects of Freon 11. The introduction of these items has resulted in a complete facility for the purpose of studying two phase flow induced vibrations. Preliminary experiments revealed a problem relating to tube tuning. Generally, the results are promising and some interesting new phenomena were observed as well. </p> / Thesis / Master of Engineering (ME)

The vehicle manufacturing sector is constantly evolving, and corporations are fully aware of increased consumer expectations for both driver and passenger´s comfort. SCANIA CV AB, as one of the largest Swedish manufacturers of commercial vehicles, has put an emphasis on this area. To guarantee these high-quality standards, several tests are conducted daily. Within this framework, this project aims to gain a better understanding of the phenomena associated with steering wheel vibrations. This project has an experimental focus on recreating sensitive driving conditions and addressing the vibration transfer paths to the main user interface such as the steering wheel. As widely known, the main problems related to vibrations come from resonance excitations. The most obvious solution would be to simply avoid matching any system´s eigenmodes with external excitations. Considering broadband excitations such as bumpy roads or engine vibrations, it is very unlikely that none of the critical frequencies is triggered. A better and more realistic idea would be minimizing the effects of these resonances by structural optimization. However, to do so, the eigenmodes should first be addressed. For this purpose, this project focused on identifying the annoying frequencies triggered while recreating sensitive driving scenarios. These sensitive scenarios were identified by Scania as circumstances in which the steering wheel feel gets altered. Specifically, it was decided to focus on road-induced vibrations, wheel-induced vibrations and engine-induced vibrations. The main findings show that during these tests, some resonances are triggered and interesting features are captured on the steering wheel. / Fordonstillverkningssektorn växer ständigt och företag är fullt medvetna om ökade konsumentförväntningar på både förarens och passagerarnas komfort. SCANIA CV AB, som en av de största svenska tillverkarna av kommersiella fordon, har lagt vikt vid detta område. För att garantera dessa högkvalitativa standarder genomförs flera tester dagligen.Inom denna ram syftar detta projekt till att få en bättre förståelse för de fenomen som är förknippade med rattvibrationer. Detta projekt har ett experimentellt fokus på att återskapa känsliga körförhållanden och adressera vibrationsöverföringsvägarna till huvudanvändargränssnittet, såsom ratten. Som allmänt känt kommer de största problemen relaterade till vibrationer från resonansexcitationer. Den mest uppenbara lösningen skulle vara att helt enkelt undvika att matcha något systems egenmoder med externa excitationer. Med tanke på bredbandsexcitationer som gropiga vägar eller motorvibrationer är det mycket osannolikt att ingen av de kritiska frekvenserna utlöses. En bättre och mer realistisk idé skulle vara att minimera effekterna av dessa resonanser genom strukturell optimering. För att göra det bör egenmoden först behandlas. För detta ändamål fokuserade detta projekt på att identifiera de irriterande frekvenser som triggades samtidigt som känsliga körscenarier återskapades. Dessa känsliga scenarier identifierades av Scania som omständigheter där rattkänslan förändras. Specifikt beslutades att fokusera på väginducerade vibrationer, hjulinducerade vibrationer och motorinducerade vibrationer. Huvudfynden visar att under dessa tester triggas vissa resonanser och intressanta funktioner fångas på ratten.

This thesis investigates the impact of vibration isolators on circuit boards during harsh vibrationenvironments that occur when they are mounted on the wings of a fighter jet. To examine thisphenomenon, a mathematical model and a simulated model were developed to determine theresonant frequencies of the circuit board under various boundary conditions. Subsequently, theresonant frequencies of the circuit board were validated through experimental tests, allowing forthe establishment of the material properties of the circuit board. In order to prevent structuralfailure, this thesis employs α-gel dampers as the damped attachments for the circuit board.These vibration isolators belong to the category of silicone gel dampers and were evaluatedthrough experimental vibration testing. The two employed vibration isolators are denoted asmodels A1 and A2, exhibiting respective damping ratios of 0.1 and 0.05. By utilizing thesevibration isolators during the experimental vibration tests, the structure demonstrated resilienceagainst natural frequency coupling, thereby preventing failure. / Den här masteruppsatsen undersöker effekten av vibrationsisolatorer på kretskort under detuffa vibrationsmiljöer som sker vid vingarna på ett stridsflyg. För att undersöka detta såanvänds en matematisk modell samt en simulerad modell för att hitta resonansfekvensernaför kretskorten vid olika randvillkor. Resonansfrekvenserna från modellerna jämfördes medresonansfrekvenserna som kom tillhanda efter vibrationsprover och med dem så kunde ävenmaterialegenskaperna bestämmas. För att unvika kollaps av strukturen användes α-geldämpare till kretskorten. Dessa dämpare är gjorde av silikongel och utvärderades genomexperimentella vibrationsprover. Dessa vibrationsisolatorer var av modell A1 och A2 ochkorresponderande modell hade dämpningsförhållande 0.1 respektive 0.05. Genom att användadessa vibrationsiolatorer under de experimentella virbationstesterna så undvek strukturenkollaps genom att resonansfrekvenserna inte triggades.

This study explores the relationship between endmill tool dynamics and cutting parameters, emphasizing the impact of these factors on machining dynamics, surface finish, and dimensional control. It introduces a novel approach to analyze and optimize the overall performance of a solid carbide endmill, with a specific focus on machining Aluminum 6066-T6. By using stability lobes diagrams (SLD), stable conditions for cutting were chosen, and then surface roughness and tool and workpiece vibration analyses were performed to assess machining performance. This work aims to understand the effects of operating below the peaks and valleys, inherent in the shape of the SLD, using different RPMs. The study's methodology involves tap tests using CutPro - Tap Test Module and milling tests on a horizontal machining center. The surface roughness measurement was performed using an Alicona Infinite Focus confocal microscope and accelerometers were positioned on the spindle bearing housing and workpiece. The findings suggest that within the stable range below the stability lobe diagram's boundary, there is a significant difference in vibration resulting in variation in surface roughness corresponding to the peaks and valleys of the SLD. The variation of acceleration, and consequently vibration, was considerably higher when operating below valleys which negatively affected the surface roughness of the workpiece. The surface roughness plays a pivotal role in tool performance and subsequently influences metal removal rate and tool and spindle life. For conditions closer to instability, this is even more important. In conclusion, this research lays the foundation for a holistic approach to solid carbide endmill design and cutting parameter selection, showing that the machining process can be optimized in terms of the SLDs, even in regions far below the stability limit / Thesis / Master of Applied Science (MASc)