This study investigates energy harvesting characteristics from a spinning device that consists of a proof mass that is supported by two orthogonal elastic structures with the piezoelectric material. Deformation in the piezoelectric structures due to vibration of the proof mass generates voltages to power electrical loads. The governing equations for this electromechanically coupled device are derived using Newtonian mechanics and Kirchhoff's voltage law. The case where the device rotates at a constant speed and is subjected to sinusoidal base excitation is examined in detail. The energy harvesting behavior is investigated for devices with identical piezoelectric support structures (called tuned devices). Closed-form expressions are derived for the steady state response and power harvested. For nonzero rotation speeds, these devices have multifrequency dynamic response and power harvested due to the combined vibration and rotation of the host system. The average power harvested for one oscillation cycle is calculated for a wide range of operating conditions to quantify the devices' performance. Resonances do not occur for cases when the base excitation frequency is fixed and the rotation speed varies. For cases of fixed rotation speed and varying base excitation frequency, however, resonances do occur. The number and location of these resonances depend on the electrical circuit resistances and rotation speed. Resonances do not occur at speeds or frequencies predicted by resonance diagrams, which are commonly used in the study of rotating system vibration. These devices have broadband speed energy harvesting ability. They perform equally well at high and low speeds; high speeds are not necessary for their optimal performance. The impact of the chosen damping model on energy harvesting characteristics for tuned devices is investigated. Two common damping models are considered: viscous damping and structural (hysteretic) damping. Closed-form expressions for steady state dynamic response and power harvested are derived for models with viscous and structural damping. The average power harvested using the model with structural damping behaves similarly at high speeds and low speeds, and at high resistances and low resistances. For the viscous damping model, however, the average power harvested is meaningfully different at high speeds compared to low speeds, and at high resistances compared to low resistances. The characteristics of devices with nonidentical piezoelectric support structures (called mistuned devices) are investigated numerically. Similar to spinning tuned devices, mistuned devices have multifrequency dynamic response and power harvested. In contrast to tuned devices, high amplitude average power harvested occurs near speeds and base excitation frequencies predicted by resonance diagram.

Using MATLAB and a National Instruments data acquisition card, a signal processing program meant to monitor the behavior of rotordynamic systems in real-time was developed and tested. By using traditional analysis methods in this field of engineering, commonly desired data representations such as bode, polar, orbit, full spectrum plots were able to be produced to a very high accuracy. Additional capabilities offered by this application are slow roll compensation, synchronous and sub-synchronous filtering, and true three dimensional plotting. The verification of this program was done by comparing the results to the ones acquired with Bently Nevada’s “Automated Diagnostics for Rotating Equipment” (ADRE) system. In addition to a data acquisition program, theoretical models of the two-disk rotor were created to estimate the unknown physical parameters of the system. By simulating the rotor with and without gyroscopic effects included, estimates for the stiffness, damping, eccentricity, initial phase, and initial skew values present in the system were determined.

Le présent document a pour objet la modélisation transitoire non linéaire du comportement vibratoire des systèmes de frein aéronautiques. Le but est de reproduire numériquement l’apparition et le niveau des vibrations au cours du temps, afin de les maîtriser et d’adapter la conception du frein. Les essais de freinage mettent en évidence deux modes de vibration que sont le whirl et le squeal. Si les niveaux de ces vibrations deviennent trop importants, la structure de la roue et du train d’atterrissage peut être endommagée. Afin d’éviter de tels dommages, la conception du frein doit être adaptée. Pour réaliser cela, Messier-Bugatti-Dowty doit disposer d’un modèle capable de prédire les niveaux de vibration du frein au cours du temps pendant la phase de freinage. Le modèle doit avoir une précision suffisante, être en lien avec la maquette numérique et ne doit pas exiger de recalage. Un premier travail vise à améliorer le modèle éléments finis existant qui se révèle être trop imprécis. Une étude portant sur les effets gyroscopiques permet d’évaluer leur impact sur la fréquence et la stabilité des modes de whirl. Une modélisation plus complète du bâti d’essai améliore la précision de la fréquence du mode de squeal. Enfin, le mode de whirl est mieux simulé grâce au développement d’un modèle de pneumatique à partir de son analyse modale. Ce modèle est ensuite réduit afin de réaliser une intégration temporelle. Une sous-structuration permet de séparer l’ensemble des disques du frein, où le frottement et la non-linéarité se situent, du reste de la structure considérée comme linéaire. Trois techniques de réduction de l’ensemble des disques sont exposées. On évalue leur représentativité par rapport au modèle non-réduit en comparant les fréquences et la stabilité des modes propres. La première méthode est une représentation nodale de l’ensemble des disques. Les équations décrivant la non-linéarité et le frottement sont analytiques. Pour la deuxième méthode, la non-linéarité est déplacée à l’extrémité de l’ensemble des disques pour la découpler du frottement. La troisième méthode, plus ambitieuse et complexe, conserve à la fois l’emplacement de la nonlinéarité aux interfaces frottantes et la géométrie des disques. Une technique de réduction modale permet d’abaisser le nombre de degrés de liberté non linéaires. Pour clore ce rapport, des simulations transitoires sont calculées à partir des modèles réduits. Des études d’influences sont réalisées. Les paramètres étudiés sont le type d’algorithme d’intégration temporelle, l’amortissement introduit, la loi non linéaire, la pression hydraulique d’entrée et le coefficient de frottement. Leurs impacts sur les niveaux et la durée d’apparition des vibrations est évalué. / This report deals with the non-linear transient simulation of the dynamic behaviour of aeronautic brake systems. The objective is to reproduce the occurrence and level of vibrations versus time in order to control and adjust design consequently. The braking tests highlight two eigenmodes, which are called whirl and squeal. If the level of these vibrations becomes too high, the structures of the wheel and the landing gear may be damaged. To avoid damage, the design has to be adjusted. To achieve this, Messier-Bugatti-Dowty requires a model that is able to predict the levels of vibrations of the brake when it is braking. This model must have an adequate accuracy, be linked to the digital mockup and not require tuning. First, the existing finite element model has to be improved because its initial accuracy is not acceptable. A study about gyroscopic effects allows to assess their impact on the frequency and the stability of whirl modes. A complete modelling of the test frame improves the squeal modes’ frequency accuracy. At last, the whirl modes are better simulated due to the development of a tyre model based on modal analysis data. Then, the finite element model is reduced in order to perform a temporal integration. A substructuring allows to separate the set of brake discs (heat sink), where friction and non-linearities are located, from the rest of the structure which is considered linear. Three heat sink reduction techniques are proposed. Their representativeness are estimated compared to the non-reduced model. The first technique is a nodal description of the heat sink. The equations of friction and non-linearity are analytical. For the second technique, the non-linearity is displaced to the extremity of the heat sink to uncouple it from friction. The third technique, more ambitious and complex, keeps the location and non-linearity in friction interfaces and discs geometry. A reduction technique enables to decrease the number of non-linear degrees of freedom. As a conclusion, transient simulations are computed from reduced models. Sensitivity studies are performed. Studied parameters are the type of integration solver, introduced damping, non-linearities, hydraulic pressure, and friction coefficient. Their impacts on level and duration of occurrence of vibrations is estimated.