abstract: Monte Carlo simulations are traditionally carried out for the determination of the amplification of forced vibration response of turbomachine/jet engine blades to mistuning. However, this effort can be computationally time consuming even when using the various reduced order modeling techniques. Accordingly, some investigations in the past have focused on obtaining simple approximate estimates for this amplification. In particular, two of these have proposed the use of harmonic patterns of the blade properties around the disk as an approximate alternative to the many random patterns of Monte Carlo analyses. These investigations, while quite encouraging, have relied solely on single degree of freedom per sector models of the rotor. In this light, the overall focus of the present effort is a revisit of harmonic mistuning of rotors focusing first the confirmation of the previously obtained findings with a more detailed model of the blisk in both conditions of an isolated blade-dominated resonance and of a veering between blade and disk dominated modes. The latter condition cannot be simulated by a single degree of freedom per sector model. Further, the analysis will consider the distinct cases of mistuning due to variations of material properties (Young's modulus) and geometric properties (geometric mistuning). In the single degree of freedom model, both mistuning types are equivalent but they are not, as demonstrated here, in more realistic models. The difference arises because changes in geometry induce not only changes in natural frequencies of the blades alone but of their modes and the importance of these two sources of variability is discussed with both Monte Carlo simulation and harmonic mistuning results. The present investigation focuses also on the possible extension of the harmonic mistuning concept and of its quantitative information that can be derived from such analyses. From it, a novel measure of blade-disk coupling is introduced and assessed in comparison with the coupling index introduced in the past. In conclusions, the low cost of harmonic mistuning computations in comparison with full Monte Carlo simulations is demonstrated to be worthwhile to elucidate the basic behavior of the mistuned rotor in a random setting. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2014

Accurate predictions of ground-borne vibration levels in the vicinity of an underground railway are greatly sought after in modern urban centers. Yet the complexity involved in simulating the underground environment means that it is necessary to make simplifying assumptions about this system. One such commonly made assumption is to ignore the effects of nearby embedded structures such as piled foundations and neighbouring tunnels. Through the formulation of computationally efficient mathematical models, this dissertation examines the dynamic behaviour of these two particular types of structures. The effect of the dynamic behaviour of these structures on the ground-borne vibration generated by an underground railway is considered. The modelling of piled foundations begins with consideration of a single pile embedded in a linear, viscoelastic halfspace. Two approaches are pursued: the modification of an existing plane-strain pile model; and the development of a fully three-dimensional model formulated in the wavenumber domain. Methods for adapting models of infinite structures to simulate finite systems using mirror-imaging techniques are described. The interaction between two neighbouring piles is considered using the method of joining subsystems, and these results are extended to formulate models for pile groups. The mathematical model is validated against existing numerical solutions and is found to be both accurate and efficient. A building model and a model for the pile cap are developed, and are attached to the piled foundation. A case study is used to illustrate a procedure for assessing the vibration performance of pile groups subject to vibration generated by an underground railway. The two-tunnel model uses the superposition of displacement fields to produce a fully coupled model of two infinitely long tunnels embedded in a homogeneous, viscoelastic fullspace. The significance of the interactions occurring between the two tunnels is quantified by calculating the insertion gains that result from the existence of a second tunnel. The results show that a high degree of inaccuracy exists in any underground-railway vibration prediction model that includes only one of the two tunnels present.

Le stockage de grains est une problématique qui date du développement de l’agriculture afin de répondre au besoin de conservation des céréales. Afin de faciliter la vidange de silos, l’entreprise Vibrafloor propose une solution de vidange automatisée basée sur l’agitation du contenu par vibration d’un plancher flexible. L’objectif de cette thèse est de développer un modèle numérique robuste qui puisse prédire le comportement du système vibrant sous charge, au cours d’un cycle de vidange. Ces travaux peuvent être décomposés en trois parties principales : - Le développement d’un modèle numérique fiable d’un module vibrant ; - Le développement d’un modèle numérique du milieu granulaire ; - La mise en interaction de ces deux modèles. Enfin, l’exploitation de ces modèles numériques a permis de proposer des règles d’utilisation du système à l’industriel et de proposer les prémisses d’un outil d’étude du procédé de vidange dans sa globalité. / The grain storage is an issue that dates agricultural development to address the need for cereal preservation. In order to facilitate the emptying silos process, Vibrafloor provides an automated emptying solution based on the agitation of the contents by vibration of a flexible floor. The objective of this thesis is to develop a reliable numerical model that can predict the behavior of the vibrating system under load during a drain cycle. These works can be divided into three main parts: - The development of a reliable digital model of a vibrating module - The development of a numerical model of the granular media - The interaction of these two models. Finally, the exploitation of these numerical models helped provide system usage rules for industrial and the beginnings of a study tool for the entire automatic drain process.