This work investigates the use of multi-degree of freedom (MDOF) passive and active vibration absorbers for the control of structural vibration as an improvement to conventional single degree of freedom (SDOF) vibration absorbers. An analytical model is first used to compare passive two degree of freedom (2DOF) absorbers to SDOF absorbers using point impedance as the performance criterion. The results show that one 2DOF absorber can provide the same impedance at two resonance frequencies as two SDOF absorbers for equal amounts of total mass. Experimental testing on a composite cylindrical shell supports the assertion that a 2DOF absorber can attenuate two resonance frequencies. Further modeling shows that MDOF absorbers can utilize the multiple mode shapes that correspond to their multiple resonance frequencies to couple into modes of a distributed primary system to improve the attenuation of structural resonance. By choosing the coupling positions of the MDOF absorber such that its mode shape mirrors that of the primary system, the mass of the absorber can be utilized at multiple resonance frequencies. For limited ranges of targeted resonance frequencies, this technique can result in MDOF absorbers providing attenuation equivalent to SDOF absorbers while using less mass. The advantage gained with the MDOF absorbers is dependent on the primary system. This work compares the advantage gained using the MDOF absorbers for three primary systems: MDOF lumped parameter systems, a pinned-pinned plate, and a cylindrical shell. The active vibration absorber study in this work is highly motivated by the desire to reduce structural vibration in a rocket payload fairing. Since the efficiency of acoustic foam is very poor at low frequencies, the target bandwidth was 50 to 200 Hz. A 2DOF active vibration absorber was desired to exhibit broad resonance characteristics over this frequency band. An analytical model was developed to facilitate the design of the mechanical and electrical properties of the 2DOF active vibration absorber, and is supported by experimental data. Eight active vibration absorbers were then constructed and used in a multiple-input multiple-output (MIMO) feed-forward control system on a mock payload fairing under high level acoustic excitation. The results show significant levels of global attenuation within the targeted frequency band. / Master of Science

Depuis ses débuts, la conception des convertisseurs électromécaniques se limitait à l'optimisation, par l'électrotechnicien, de la conversion d'énergie électrique en énergie mécanique. Cette énergie, alors fournie sous la forme quasi exclusive d'un mouvement à un seul degré de liberté, le plus souvent rotatif, devait ensuite être adaptée, par les mécaniciens, aux besoins du système à actionner. Aujourd'hui, grâce aux évolutions récentes dans des domaines aussi variés que l'électronique de puissance, l'informatique ou encore la conception et la fabrication assistées par ordinateur, il est devenu possible de concevoir de nouveaux actionneurs directement en fonction des besoins des applications auxquelles ils sont destinés. Ainsi, des actionneurs pouvant posséder plusieurs degrés de liberté, tant en rotation qu'en translation, ont été développés. Dans ce contexte, cette thèse poursuit deux objectifs. Le premier est de proposer une démarche de conception intégrant au mieux les aspects électriques et mécaniques de systèmes électromécaniques tels que ces nouveaux actionneurs. Plus largement, elle a pour vocation de s'appliquer à tous types de problèmes multidisciplinaires où la prise en compte des différentes disciplines et de leurs interactions est indispensable pour assurer les performances globales du produit final. Plus particulièrement, elle est adaptée aux cas de recherches qui, contrairement aux cas de développements, font parfois intervenir des concepts mal maîtrisés. Le second objectif est d'appliquer cette démarche à la conception d'un actionneur électrique dont le rotor, de forme sphérique, est actionné avec un débattement illimité selon deux des trois degrés de liberté qu'il possède en rotation. Suivant les différentes étapes constituant cette démarche, divers concepts de solution sont d'abord générés, tant pour les aspects électriques d'actionnement que pour les aspects mécaniques de guidage. Ces concepts sont ensuite caractérisés, via une série de modélisations et d'expérimentations, avant d'être combinés en vue de produire une solution globale, dimensionnée, fabriquée et validée sur un banc d'essai. / From the outset, the design of electromechanical converters was limited to the optimization, by electrical engineers, of the conversion of electrical energy to mechanical energy. The latter was at that time nearly exclusively provided under the form of single degree of freedom motion, more often rotary, and had to be adapted, by mechanical engineers, to the needs of the system to be actuated. Today, thanks to recent evolutions in fields as various as power electronics, computer capabilities or computer-aided design and manufacturing (CAD-CAM), it has become possible to design new actuators by taking directly into account the needs of the applications they are intended for. As a result, actuators with several degrees of freedom, both in rotation and in translation, have been developed. Within this context, this thesis pursues two objectives. The first consists in proposing a new design method integrating as best as possible the electrical and mechanical aspects of electromechanical systems such as these new actuators. More broadly, its vocation is to be applicable to all multidisciplinary problems where taking into account each discipline and their interactions are necessary to ensure the global performances of the final product. More particularly, this method is adapted to the case of researches that, contrary to the case of other developments, sometimes includes badly mastered concepts. The second aim is to apply this approach to the design of an electrical motor with a spherical rotor actuated, with an unlimited angular range, along two of the three degrees of freedom it possesses in rotation. Following the basic steps involved in this approach, various solution concepts were first generated both for the electrical actuation aspects and the mechanical guiding aspects. These concepts were then characterized, via a number of modeling and experimentation phases, before being combined in order to obtain a global solution, which was then sized, manufactured and validated on a test bench.

In this study analysis and design procedures of partially compliant mechanisms using two degree of freedom mechanism model are developed. The flexible segments are modeled as revolute joints with torsional springs. While one freedom is controlled by the input to the mechanism, the motion of the parts are governed both by the kinematics and the force balance. The procedure developed for the analysis of such mechanisms is shown on two different mechanisms: a five link mechanism with crank input and slider output (five-bar mechanism) / a five link mechanism with crank input and rocker output. Design charts are prepared according to output-link oscillation and dimensionless design parameters

This student thesis aims to analyze the unbalance on rotating machinery by simulation and experimental. The machinery flywheel rotation is modelled as a Single Degree of Freedom (SDOF) and Multi Degree of Freedom (MDOF) system. The model rotation unbalance is simulated by MATLAB. Then the vibration measurement is taken by experimental. In addition, the tachometer is used to determine the flywheel speed calibration. Finally, the rotating unbalance reduction simulation is performed with different parameter value to determine an optimum level of machinery rotation vibration. Unbalance on rotating machinery causes a harmful influence on the environment and machinery. The root cause of rotating unbalance is determined by the simulation and experimental analysis. The analysis result is used as an indicator for predicting machinery breakdown and estimating the correct predictive maintenance action for the machinery. In this project, the simulation and experimental analysis were carried out on a rotating component of the KICKR Snap Bike Trainer. The simulation and numerical analysis are performed by MATLAB programme. On the experimental part, the vibration measurement method and results were discussed. The suggestion of unbalance reduction were recommended base on measurement and vibration analysis results.

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This thesis presents a technique for the optimal synthesis of planar five-link mechanisms that produce a desired mechanical advantage function over a specified path. Since a five-bar linkage has two degrees of freedom, small deviations from the specified path are possible without significantly altering the mechanical advantage function. The research shows one potential application, the design of strength machines, where it is important to control force while allowing the user freedom of motion. In the past, closed-form analytical synthesis techniques have been used to design mechanical-advantage-generating linkages. This method is time consuming and case specific. However, optimal synthesis techniques apply to the general case and present a robust solution procedure. This thesis uses the non-linear pattern search technique of Hooke and Jeeves to synthesize five-bar linkages. The search technique matches user strength curves and mechanism resistance curves to produce a five-link mechanism. This mechanism produces the desired mechanical-advantage function and serves as the basis for strength training machines. Unlike analytical synthesis, optimization allows direct incorporation of a greater number of design constraints, thus resulting in solutions that are more practical. The pattern search technique aims to minimize a given objective function that depends primarily on the force generating capabilities and kinematic constraints on of the linkage. / Master of Science

no / The paper deals with the problem of predicting the maximum response statistics of Multi-Degree-of-Freedom (MDoF) linear structures subjected to non-stationary non-white noises. The extension of two different censored closures of Gumbel type, originally proposed by the authors for the response of Single-Degree-of-Freedom oscillators, it is presented. The improvement associated with the introduction in the closure of a consistent censorship factor, accounting for the response bandwidth, it is pointed out. Simple and effective step-by-step procedures are formulated and described in details. Numerical applications on a realistic 25-storey moment-resisting frame along with comparisons with classical approximations and Monte Carlo simulations are also included.

Master of Science / Department of Civil Engineering / Hani G. Melhem / The objective of this research is to use structure ambient random vibration response to detect damage level and location. The use of ambient vibration is advantageous because excitation is caused by service conditions such as normal vehicle traffic on a highway bridge, train passage on a railroad bridge, or wind loads on a tall building. This eliminates the need to apply a special impact or dynamic load, or interrupt traffic on a bridge in regular service. This research developed an approach in which free vibration of a structure is extracted from the response of this structure to a random excitation in the time domain (acceleration versus time) by averaging out the random component of the response. The result is the free vibration that includes all modes based on the sampling rate on time. Then this free vibration is transferred to the frequency domain using a Fast Fourier Transform (FFT). Variations in frequency response are a function of structural stiffness and member end-conditions. Such variations are used as a measure to identify the change in the structural dynamic properties, and ultimately detect damage. A physical model consisting of a 20 × 20 × 1670 -mm long steel square tube was used to validate this approach. The beam was tested under difference supports conditions varying from a single- to three-span continuous configuration. Random excitation was applied to the beam, and the dynamic response was measured by an accelerometer placed at various locations on the span. A numerical model was constructed in ABAQUS and the dynamic response was obtained from the finite element model subjected to similar excitation as in the physical model. Numerical results were correlated against results from the physical model, and comparison was made between the different span/support configurations. A subsequent step would be to induce damage that simulates loss of stiffness or cracking condition of the beam cross section, and that would be reflected as a change in the frequency and other dynamic properties of the structure. The approach achieved good results for a structure with a limited number of degrees of freedom. Further research is needed for structures with a larger number of degrees of freedom and structures with damage in symmetrical locations relative to the accelerometer position.

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