Actuating a cantilever piezoelectric element over a frequency spectrum, the movement will show resonances and hysteresis behavior not present in the input signal. Excursion modeling and open loop control of a cantilever piezoelectric bimorph actuator was studied in this thesis, with the aim to enhance the actuator's movement to more accurately render audible input. This actuator has lower energy consumption and presents new possibilities for speaker design in constrained situations compared to conventional micro speaker technology. Much work has previously been done to model piezoelectric cantilever actuators below the first and second resonance frequency. This thesis describes a physical linear model and its modifications to render the eight first resonance frequencies below 20 kHz, as well as the model's performance in open loop control. This was performed on a single piezoelectric beam and a concept piezoelectric speaker. For the single piezoelectric beam the model was validated with fair overall result below 3 kHz. The model is suggested to have fair overall behavior up to 15 kHz. Above 15 kHz the experiments showed changed characteristics that were not modeled well. The open loop control had the intended behavior but severe resonances and physical constraints made the open loop control ineffective to enhance the sound rendering. Two different approaches were used for trying to improve the sound rendering based on an excursion model. These approaches did not generate useful methods but present viable input to future work with this type of speaker structure, for reducing disharmonics and creating a physical design tool for sound simulation. For the concept piezoelectric speaker, due to difficulties in measuring excursion, the model could not be validated. This made the approaches for enhancing the sound rendering ineffective. However, it can be concluded from the concept speaker that the cantilever piezoelectric speaker technology has qualities that could compete with the conventional micro speaker technology. Challenges remain in electric hardware, actuator configuration and acoustic design as well as in fine tuned signal processing for the concept speaker to become a competitive product.

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<p>The Mechanics of Structural Genome (MSG) is a unified homogenization theory used to find equivalent constitutive models for beam, plate, and solid structures. It has been proven accurate for periodic structures. However, for certain applications such as non-prismatic wind turbine blades and helicopter flexbeams featuring ply drop-off, where there is no repeating structure and the periodic boundary condition cannot be used, MSG's accuracy is limited. In this work, we aim to extend MSG to find element stiffness matrices directly for aperiodic structures, instead of beam properties or three-dimensional (3D) solid material properties. Two finite elements based on MSG have been developed: Heterogeneous Beam Element (HBE) and Heterogeneous Solid Element (HSE).</p> <p><br></p> <p>For beam modeling, the beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18×18 effective beam element stiffness matrices. These matrices are used as input for one-dimensional (1D) beam analysis using the Abaqus User Element subroutine (UEL). Using the macroscopic beam analysis results as input, we can also perform dehomogenization to predict the stresses and strains in the original structure. We use three examples (a prismatic composite beam, an isotropic homogeneous tapered beam, and a composite tapered beam) to demonstrate the capability of HBE and show its advantages over the MSG cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry.</p> <p><br></p> <p>The Heterogeneous Solid Element (HSE) is developed based on MSG to model a heterogeneous body as an equivalent solid element using an effective element stiffness matrix. HSE modeling includes homogenization, macroscopic global analysis, and dehomogenization to recover local strains/stresses. HSE avoids the local periodicity assumption for traditional multiscale modeling techniques for composite structures that compute effective material properties instead. Abaqus composite solid element and MSG-based traditional multiscale modeling are used to validate the accuracy of HSE. All example results show that HSE is more accurate in predicting global structural behavior and local strains/stresses.</p> <p><br></p> <p>HBE and HSE provide a new concept for modeling aperiodic composite structures by modeling structures into equivalent beam or solid elements instead of beam properties of the reference line in 1D beam analysis or material properties of material points in solid structural analysis.</p>

L’appareil de radiochirurgie CyberKnife performe des traitements avancés de radiothérapie qui offrent des avantages nets pour certains types de cancer. Or, cet appareil produit uniquement des petits faisceaux circulaires ce qui complexifie les procédures de dosimétrie en milieu clinique. En effet, en conditions de petits champs, les diverses perturbations au niveau du détecteur peuvent être très grandes. Ainsi, l’utilisation de la méthode Monte Carlo est nécessaire lors de l’étalonnage et la caractérisation de faisceaux. Ces processus, lors desquels des valeurs de dose de référence et relative sont mesurées et entrées dans les systèmes de planification de traitement, assurent l’efficacité des traitements ainsi que la sécurité des patients. Cette thèse porte sur la modélisation Monte Carlo du CyberKnife M6 et étudie diverses applications à la dosimétrie de petits champs de radiothérapie. En premier lieu, une nouvelle méthode permettant la correction de la dépendance au débit de dose des diodes au silicium est proposée. Cette dernière est validée puis appliquée à des mesures relatives effectuées au CyberKnife du Centre hospitalier de l’Université de Montréal (CHUM). Les résultats illustrent la correction de l’erreur systématique induite dans les mesures due à la dépendance au débit de dose de la diode considérée. La méthode proposée fournit alors une solution efficace à cette problématique. En second lieu, une méthode pour l’optimisation des paramètres sources requis en entrée lors de la modélisation Monte Carlo de faisceaux de radiothérapie est introduite. Cette dernière est basée sur une approche probabiliste portant sur la comparaison de mesures et de simulations pour divers détecteurs, et permet la détermination de l’énergie du faisceau d’électrons incident sur la cible d’un appareil, ainsi que de la largeur à mi-hauteur de sa distribution radiale. La méthode proposée, qui est appliquée au CyberKnife du CHUM, fournit une nouvelle approche permettant l’optimisation d’un modèle Monte Carlo d'un faisceau ainsi que l’estimation des incertitudes sur ses paramètres sources. En troisième lieu, le modèle de faisceau du CyberKnife développé est utilisé afin d’estimer l’impact des incertitudes des paramètres sources sur diverses fonctions dosimétriques couramment utilisées en milieu clinique, ainsi que sur des distributions de dose obtenues par simulation de plans de traitement. Les résultats illustrent l’augmentation de l’impact des incertitudes du modèle de faisceau avec la réduction de la taille de champ, et fournissent une nouvelle perspective sur la précision de calcul atteignable pour ce type de calcul de dose Monte Carlo en petits champs. En quatrième lieu, les protocoles de dosimétrie TG-51 (version adaptée du manufacturier) et TRS-483 sont respectivement appliqués et comparés pour l’étalonnage du CyberKnife M6 se trouvant au CHUM. Il est observé que le TRS-483 est cohérent avec le TG-51. Des facteurs de correction de la qualité et corrigeant pour les effets de moyenne sur le volume propres au CyberKnife du CHUM sont estimés par simulations Monte Carlo pour une chambre à ionisation Exradin A12. Les résultats illustrent que la valeur générique fournie dans le TRS-483 pourrait être surestimée en comparaison à notre modèle de CyberKnife et que cette surestimation pourrait être due à la composante de moyenne sur le volume. / The CyberKnife radiosurgery system performs advanced radiotherapy treatments that offer clear benefits for certain types of cancer. However, this device produces small circular fields only, which complicates dosimetry procedures in a clinical environment. Indeed, under small field conditions, the various perturbations at the detector level can become very large. Thus, the use of the Monte Carlo method is necessary when calibrating and characterizing beams. Such processes, during which reference and relative dose values are measured and entered into treatment planning systems, ensure the validity of treatments as well as patient safety. This thesis focuses on the Monte Carlo modeling of the CyberKnife M6 and studies various applications to small photon fields dosimetry. Firstly, a new method for the correction of the dose rate dependency of silicon diode detectors is proposed. The latter is validated and applied to relative measurements performed at the CyberKnife of the Centre hospitalier de l’Université de Montréal (CHUM). Results illustrate the correction of the systematic error induced in the measurements due to the dose rate dependency of the considered diode. The proposed method provides an efficient solution to this issue. Secondly, a method for the optimization of the source parameters required as input during Monte Carlo beam modeling is introduced. The latter is based on a probabilistic approach and on the comparison of measurements and simulations for various detectors. The method allows the determination of the energy of the electron beam incident on the target of a linac, as well as the full width at half-maximum of its radial distribution. The proposed method, which is applied to the CyberKnife unit of the CHUM, provides a new approach for the optimization of a Monte Carlo beam model and a way to estimate the uncertainties on its source parameters. Thirdly, the developed CyberKnife beam model is used to estimate the impact of source parameter uncertainties on various dosimetric functions commonly used in the clinic environment, and on dose distributions obtained by simulation of treatment plans. Results illustrate the increase of the impact of beam modeling uncertainties with the decrease of the field size, and provide insights on the reachable calculation accuracy for this type of Monte Carlo dose calculation in small fields. Lastly, the TG-51 (manufacturer’s adapted version) and TRS-483 dosimetry protocols are respectively applied and compared for the calibration of the CHUM’s CyberKnife. We observe that TRS-483 is consistent with TG-51. Beam quality and volume averaging correction factors specific to the CHUM's CyberKnife are estimated using Monte Carlo simulations for an Exradin A12 ionization chamber. Results illustrate that the generic value provided in the TRS-483 could be overestimated in comparison to our CyberKnife model and that this overestimation could be due to the volume averaging component.