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In this thesis, the author presents a numerical and experimental study of the application of active constrained layer damping to a clamped-clamped plate. Piezoelectric actuators with modal controllers are used to improve the performance of vibration suppression from the passive constrained layer damping treatment. Surface damping treatments are often effective at suppressing higher frequency vibrations in thin-walled structures such as beams, plates and shells. However, the effective suppression of lower frequency modes usually requires the additional of an active vibration control scheme to augment the passive treatment. Advances in the technologies associated with so-called smart materials are dramatically reducing the cost, weight and complexity of active structural control and make it feasible to consider active schemes in an increasing number of applications. Specifically, a passive constrained layer damping treatment is enhanced with an active scheme employing a piezoceramic (PZT) patch as the actuator. Starting with an established finite element formulation it is shown how model updating and model reduction are required to produce a low-order state-space model which can be used as the basis for active control. The effectiveness of the formulation is then demonstrated in a numerical study. Finally, in the description of the experimental study it is shown how modes in the frequency range from 0 to 600 Hz are effectively suppressed: the two lowest modes (bending and torsional) through active control, the higher modes (around ten in number) by the passive constrained damping layer. The study'S original contribution lies in the experimental demonstration that given a sufficiently accurate model of the plate and passive constrained damping layer, together with a suitable active feedback control algorithm, spillover effects are not significant even when using a single sensor and single actuator. The experimental traces show, in some instances, minor effects due to spillover. However, it can be concluded that the presence of the passive layer introduces sufficient damping into the residual modes to avoid any major problems when using only the minimum amount of active control hardware.

The subject of this thesis is about the balancing of large flexible rotors which exhibit mixed modal characteristics. The objective of the research was to develop a balancing procedure to determine correction masses without trial runs. This required the determination of(a) the modal vibration vectors for each resonance, (b) the modal damping ratios,(c) the mode shapes and(d) the equivalent mass of the rotor for each mode. It was made clear from the beginning that trial runs are unavoidable either, when the mode shapes cannot be determined using an analytical or numerical method, or when there is dual vibration at normal operating speed, produced by the influence of higher unbalanced modes, is too high to allow continuous operation of the machine. Therefore, the scope of the project was limited to the possible determination of correction masses without trial runs for the vibration modes included within the normal operating range. Some studies about the minimisation or complete elimination of trial runs have been published by several authors, but a literature search revealed no reports of systematic application of these procedures to field balancing of large turbo generators. This suggested that some practical difficulties had still to be overcome, opening the possibility for further research on this area. Analysis of the rotor response demonstrated the necessity of considering the angular position of the transducers when registering the rotor vibration. It was shown that measuring in a direction other than those of the principal axes of stiffness introduces errors when determining the magnitude and phase of the correction masses. That is to say, failing to consider the effects of the transducer angular position eliminates the possibility of balancing the rotor without trial runs. This is the first time that this problem has been recognised. The procedure developed was verified using an experimental rotor rig. The successful application of the procedure to the balancing of this rotor demonstrates that balancing withouttrialrunsisnotonlyatheoreticalbutalsoapracticalpossibility. The dynamic characteristics of the rotor rig, however, were some what limited and did not cover all the possibilities considered during the project. Therefore, a more complete numerical example was also successfully solved using the computer model of a rotor with characteristics similar to those of a real turbine, and whose unbalanced distribution was not initially known by this author.

Vehicle vibration is inherently random and non-stationary with a non-Gaussian distribution. In addition, variations in vehicle parameters, product payloads and distribution journeys mean that the characteristics of vibration are not identical for all distribution journeys. Because vehicle vibration and shock are key causes of damage during distribution, their simulation in pre-distribution testing is vital in order to ensure that adequate protection is provided for transported products. The established method set out in the current testing standards utilises a global set of averaged accelerated power spectral density spectra to construct random vibration signals. These signals are stationary with Gaussian distributions and, therefore, do not fully represent actual vehicle vibration, only an average. The aim of the investigation, reported on in this Thesis, was to create an improved test regime for simulating vehicle vibration for pre-distribution testing of packaging. This aim has been achieved through the construction of representative tests and the creation of realistic simulations with statistical significance. A journey database has been created, in which historic road profile data along with a quarter vehicle model have been used to approximate a known vehicle’s vibration on a specific distribution journey. Additionally, a wavelet decomposition method, in which wavelet analysis is used to decompose the approximate vehicle vibration in to a series of Gaussian approximations of varying amplitude and spectral content, has been developed. Along with theoretical work, case studies have been undertaken in order to validate the test regime.

L’objet de cette thèse est d’étudier différents dispositifs d’amortissement de vibrations en basses fréquences des aubes de rotor de soufflante ("fan") d’un turboréacteur. Les solutions étudiées utilisent des pastilles piézoélectriques, liées à l’aube et connectées à un circuit électrique passif ou semi-passif. Dans la première partie, il s’agit de mettre en pratique le modèle électromécanique développé dans la thèse de Julien Ducarne, puis de l’étendre au cas tridimensionnel par l’utilisation de la méthode des éléments finis. Ce modèle de comportement prend en compte le couplage entre une structure mécanique quelconque et des pastilles piézoélectriques planes ou courbes. Par la suite, un modèle réduit à faible nombre de degrés de liberté est construit, ce qui permet après résolution de prédire l’efficacité des dispositifs amortissants. Deux techniques, nommées "shunt" et "switch" sont appliquées au cas d’une aube fan. La première consiste à utiliser un circuit électrique résistif ou résonant. La seconde, encore à l’état de recherche, comporte un circuit muni d’un interrupteur synchronisé aux oscillations de la structure, ce qui produit un amortissement analogue à celui d’un frottement sec. La modélisation et l’optimisation électrique de ces circuits, issus de différents travaux antérieurs, ne font l’objet que d’un rappel dans ce mémoire. Une procédure d’optimisation est développée pour pouvoir trouver les géométries et les emplacements des pastilles qui maximisent le couplage électromécanique. Deux algorithmes différents (recuit simulé et recherche avec liste taboue) sont utilisés et mis en interaction avec les outils de calcul éléments finis pour trouver des solutions optimisées. Afin de valider sur un cas industriel l’ensemble des travaux sur les dispositifs piézoélectriques, une campagne d’essai est menée sur une aube fan de CFM56-7b. Les niveaux d’atténuation mesurés et ceux prévus par le modèle sont ensuite comparés. La seconde partie est consacrée à l’évaluation de l’effet des nonlinéarités géométriques sur la dynamique d’une structure tournante. Initialement prévue pour être intégrée à la partie shunt piézoélectrique, ceci afin de pouvoir estimer l’efficacité de ce dernier lorsque la structure tourne et vibre en grande amplitude, l’étude n’a pas été poursuivie et constitue une partie sans lien avec les techniques de réduction de vibrations. Néanmoins, les résultats obtenus en 1D, ainsi que la méthode de prise en compte des nonlinéarités dans le cas 3D viennent compléter et enrichir les différentes études actuelles menées sur le sujet, raison pour laquelle ce chapitre a été ajouté à ce mémoire. La détermination des caractéristiques dynamiques modales et leurs évolutions en fonction de certains paramètres de fonctionnement de l’aube constituent l’objet de cette partie. Plusieurs modèles sont développés et comparés pour pouvoir juger de la présence et de l’importance des divers phénomènes non linéaires dans la réponse forcée d’une poutre en rotation. / Vibration reduction of a turbojet fan blade with piezoelectric patches connected to a passive or semipassive electrical circuit, commonly called "shunt", is addressed in this study. The purpose of this work is to present a method for maximizing the performance of piezoelectric shunts. To validate the model, 2 experiments on a CFM56-7b fan blade are then done. To improve the damping level, a key issue is the optimization of the whole system, in terms of location and size of the piezoelectric patches and electric circuit components choice. It was shown these two optimizations, mechanical and electrical, can be realized separately. Moreover, it is proved the only parameters to maximize are the modal electromechanical coupling factors, which characterize the energy exchanges between the mechanical structure and the piezoelectric patches for a given mode. Since the optimal value of the electric circuit parameters are known as functions of the coupling factors and the system structural characteristics, they can be evaluated in a second step. Thus, the mechanical optimization consists in maximizing the coupling factors by optimizing the patches positions and dimensions, i.e. finding the best design. To fulfill this requirement and in order to manage a complex geometry, a 3D finite element formulation of the coupled electromechanical problem is derived from the one developed by Julien Ducarne during his Ph.D. thesis. A reduced order model of the discretized problem is then obtained by expanding the mechanical displacement unknowns vector onto the short-circuit eigenmodes to get the modal electromechanical coupling factors. However, when the optimization aims to reduce the vibration level with several patches, the main concern arises from the huge number of possible designs to test. For that reason, a method is proposed to cut back simulations time as well as to cope with the many local minima. This method consists in splitting up the optimization procedure in two steps. In the first one, the influence of patches on the structural eigenmodes is neglected. Therefore, an analytic coupling indicator, based on the eigenmodes of the naked host structure, can be defined and gives rise to a first approximate optimization using a simulated annealing algorithm. Then, the solutions of the first step are used as a starting point for a second optimization, working with the tabu search algorithm and where eigenmodes are computed for each new tested design.