The numerical simulation of elastic wave propagation in unbounded media is a topical issue. This need arises in a variety of real life engineering problems, from the modelling of railway- or machinery-induced vibrations to the analysis of seismic wave propagation and soil-structure interaction problems. Due to the complexity of the involved geometries and materials behavior, modelling such situations requires sophisticated numerical methods. The Boundary Element method (BEM) is a very effective approach for dynamical problems in spatially-extended regions (idealized as unbounded), especially since the advent of fast BEMs such as the Fast Multipole Method (FMM) used in this work. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundary (i.e. a surface in 3-D) and accounts implicitly for the radiation conditions at infinity. As a main disadvantage, the BEM leads a priori to a fully-populated and (using the collocation approach) non-symmetrical coefficient matrix, which make the traditional implementation of this method prohibitive for large problems (say O(106) boundary DoFs). Applied to the BEM, the Multi-Level Fast Multipole Method (ML-FMM) strongly lowers the complexity in computational work and memory that hinder the classical formulation, making the ML-FMBEM very competitive in modelling elastic wave propagation. The elastodynamic version of the Fast Multipole BEM (FMBEM), in a form enabling piecewise-homogeneous media, has for instance been successfully used to solve seismic wave propagation problems in a previous work (thesis dissertation of S. Chaillat, ENPC, 2008). This thesis aims at extending the capabilities of the existing frequency-domain elastodynamic FMBEM in two directions. Firstly, the time-harmonic elastodynamic ML-FMBEM formulation has been extended to the case of weakly dissipative viscoelastic media. Secondly, the FMBEM and the Finite Element Method (FEM) have been coupled to take advantage of the versatility of the FEM to model complex geometries and non-linearities while the FM-BEM accounts for wave propagation in the surrounding unbounded medium. In this thesis, we consider two strategies for coupling the FMBEM and the FEM to solve three-dimensional time-harmonic wave propagation problems in unbounded domains. The main idea is to separate one or more bounded subdomains (modelled by the FEM) from the complementary semi-infinite viscoelastic propagation medium (modelled by the FMBEM) through a non-overlapping domain decomposition. Two coupling strategies have been implemented and their performances assessed and compared on several examples

Boundary shape optimization is a technique to search for an optimal shape by modifying the boundary of a device with a pre-specified topology. We consider boundary shape optimization of acoustic horns in loudspeakers and brass wind instruments. A horn is an interfacial device, situated between a source, such as a waveguide or a transducer, and surrounding space. Horns are used to control both the transmission properties from the source and the spatial power distribution in the far-field (directivity patterns). Transmission and directivity properties of a horn are sensitive to the shape of the horn flare. By changing the horn flare we design transmission efficient horns. However, it is difficult to achieve both controllability of directivity patterns and high transmission efficiency by using only changes in the horn flare. Therefore we use simultaneous shape and so-called topology optimization to design a horn/acoustic-lens combination to achieve high transmission efficiency and even directivity. We also design transmission efficient interfacial devices without imposing an upper constraint on the mouth diameter. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter. We optimize brasswind instruments with respect to its intonation properties. The instrument is modeled using a hybrid method between a one-dimensional transmission line analogy for the slowly flaring part of the instrument, and a finite element model for the rapidly flaring part. An experimental study is carried out to verify the transmission properties of optimized horn. We produce a prototype of an optimized horn and then measure the input impedance of the horn. The measured values agree reasonably well with the predicted optimal values. The finite element method and the boundary element method are used as discretization methods in the thesis. Gradient-based optimization methods are used for optimization, in which the gradients are supplied by the adjoint methods.

Cavitation is the spontaneous vaporisation of a liquid to its gaseous state due to the local absolute pressure falling to the liquid's vapour pressure (Douglas, Gasiorek et al. 1995). Cavitation is present in a wide range of mechanical systems ranging from ship screws to journal bearing. Generally, cavitation is unavoidable and may cause considerable damage and efficiency losses to these systems. This thesis considers hydraulic systems specifically, and uses a modified Greens equation to develop a boundary integral method to simulate the effect that suspended solid bodies have on a single cavitation bubble. Because of the limitations of accurately modelling cavitation bubbles beyond touchdown, results are only presented for cases up to touchdown. The aim of the model is to draw insight into the reasons there is a measurable change in cavitation erosion rate with increasing oil-in-water emulsion percentage. This principle was extended to include the effect that ingested particulates may have on cavitation in hydraulic machinery. Two particular situations are modelled; the first consists of stationary rigid particles in varying proximity to a cavitation bubble near a rigid boundary. The second case is similar; however the suspended particle is allowed to move under the influence of the pressure differential caused by the expanding/contracting cavitation bubble. Numerous characteristics of the domain are considered, including domain pressures and fluid field motion, and individual boundary surface characteristics. The conclusion of the thesis is that solid bodies, either stationary or moving, have little effect on the cavity from an energy perspective. Regardless of size or density, all energy transferred from the cavity to the solid body is returned indicating that there is no net change. As this energy is ultimately responsible for the peak pressure experienced by the domain (and hence responsible for eroding the rigid boundary) as the cavity rebounds, it then serves that a cavity with a solid body will rebound at the same pressure as a cavity without a suspended body present. If this is coupled with the observation that the cavity centroid at touchdown is largely unaffected by the presence of a suspension, then it would appear that the bubble near a solid would rebound at a very similar position as a cavity without a solid. Consequently, the damage potential of a cavity is unaffected by a suspension. However, there is one point of contention as the profile of the re-entrant jet of the cavity is altered by the presence of a suspension. As energy is radiated away from the cavity during penetration, it is possible that the shape of the jet may alter the rate that energy is radiated away during penetration. However, this requires further research to be definitive.

With the advent of power electronics, inverter-driven induction motor are finding increased use in industries because of applications that demand variable speed operations and because of the potential savings in energy usage. However, these drives sometimes produce unacceptably high levels in vibration and acoustic noise. A literature survey has revealed that while there has been intensive research on the design of inverters to minimize acoustic noise radiation from these drives, the vibro-acoustic behaviour of an induction motor structure has received relatively little attention. The primary objective of this research project, therefore, is to develop a general strategy/algorithm for estimating the acoustic noise radiated from inverter-driven induction motors. By using a three-phase, 2.2 kW induction motor, the vibration modes due to various structural components (such as the rotor, the stator/casing, the endshields and the base plate) of the motor structure were analysed by experimental modal testing. Results indicate that the vibration modes due to the rotor are only important at low frequencies. It has been found that the power injection method gives more accurate measurement of the damping of a motor structure than the modal testing and the time decay methods. If a point force excitation is used, then it is more accurate to measure the sound radiation efficiency than the power conversion efficiency for motor structures. The effect of three different inverter designs (an ideal ???almost sinusoidal??? controller and two commercially available PWM inverters) on the radiated acoustic power were assessed for both no-load and load conditions using sound intensity measurements conducted in an anechoic room. The results indicate that although the sound power level due to aerodynamic and mechanical noise increases at a rate of 12 dB per doubling of the motor speed, the electromagnetic noise dominates at low motor speeds and is still a significant noise source even at high motor speeds. For inverters with low switching frequencies, the radiated sound power level is almost 15 dB higher than the ideal case at low speeds and is relatively insensitive to the motor speed. For inverters that implement the random modulation technique, the change in the total sound power level with the level of the random modulation is very small but the tonal nature of the noise is greatly reduced. The vibration behaviour of a motor structure was modeled using the finite element method (FEM) and validated using the experimental modal testing results. It has been found that it is essential to model the laminated stator as an orthotropic structure. While the details of other structural components (such as the endshields, the teeth in the stator and the windings) are not so important, it is essential that they are incorporated into the structural model as simplified structures to account for their mass, stiffness and boundary conditions imposed on the motor structure. Based on this structural model, the radiated acoustic power for various operating conditions has been predicated using the boundary element (BEM) and the electromagnetic force calculated from an electromagnetic finite element model. The predicted results agree reasonably well with experimental measurements. Despite the success of the FEM/BEM approaches, they can be prohibitively expensive (in terms of computer resources required) to apply to large motors and high frequencies. Thus the feasibility of using a statistical method, namely, the statistical energy analysis (SEA), to estimate the radiated acoustic sound power from an inverter-driven induction motor has been examined. In order to carry out this analysis, analytical expressions for calculating the natural frequencies and radiation efficiency of finite length circular cylindrical shells (which are simplified models of the stator and casing of a motor structure) were firstly derived. The internal loss factors and coupling loss factors of the motor structure were determined experimentally using the power injection method. Then by introducing an equivalent surface mobility of circular cylindrical shells for the electromagnetic force, the vibration response and the acoustic noise radiated from each part of the motor structure were estimated. Results indicate that SEA method is potentially an efficient and effective tool in estimating the noise radiated from inverter-driven induction motors.

[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Geological Sciences and Environmental Studies, 2007. / Includes bibliographical references (leaves 308-314).

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Neste trabalho é descrita a teoria necessária para a obtenção da grandeza denominada intensidade supersônica, a qual tem por objetivo identificar as regiões de uma fonte de ruído que efetivamente contribuem para a potência sonora, filtrando, consequentemente, a parcela referente às ondas sonoras recirculantes e evanescentes. É apresentada a abordagem de Fourier para a obtenção da intensidade supersônica em fontes com geometrias separáveis e a formulação numérica existente para a obtenção de um equivalente à intensidade supersônica em fontes sonoras com geometrias arbitrárias. Este trabalho apresenta como principal contribuição original, uma técnica para o cálculo de um equivalente à intensidade supersônica, denominado aqui de intensidade acústica útil, capaz de identificar as regiões de uma superfície vibrante de geometria arbitrária que efetivamente contribuem para a potência sonora que será radiada. Ao contrário da formulação numérica existente, o modelo proposto é mais direto, totalmente formulado na superfície vibrante, onde a potência sonora é obtida através de um operador (uma matriz) que relaciona a potência sonora radiada com a distribuição de velocidade normal à superfície vibrante, obtida com o uso do método de elementos finitos. Tal operador, chamado aqui de operador de potência, é Hermitiano, fato crucial para a obtenção da intensidade acússtica útil, após a aplicação da decomposição em autovalores e autovetores no operador de potência, e do critério de truncamento proposto. Exemplos de aplicações da intensidade acústica útil em superfícies vibrantes com a geometria de uma placa, de um cilindro com tampas e de um silenciador automotivo são apresentados, e os resultados são comparados com os obtidos via intensidade supersônica (placa) e via técnica numérica existente (cilindro), evidenciando que a intensidade acústica útil traz, como benefício adicional, uma redução em relação ao tempo computacional quando comparada com a técnica numérica existente. / This work describes the theory necessary to obtain the greatness called supersonic intensity, which aims to identify the regions of a sound source that effectively contribute to the sound power radiated, filtering recirculating and evanescent sound waves. The Fourier approach to obtain the supersonic intensity in sources having separable geometries, and the existent numerical formulation to obtain an equivalent to supersonic intensity on noise sources with arbitrary geometry. This work presents a new numeric technique for the computation of the numerical equivalent to the supersonic acoustic intensity. The technique provides the identification of the regions of a noise source with arbitrary geometry that effectively contribute to the sound power radiated to the far field by filtering recirculating and evanescent sound waves. The proposed technique is entirely formulated on the vibrating surface. The acoustic power radiated is obtained through a numerical operator that relates it with the distribution of superficial normal velocity, which is obtained by the boundary element method. Such power operator, possesses the property of being Hermitian. The advantage of this characteristic is that their eigenvalues are real and their eigenvectors form an orthonormal set for the velocity distribution. It is applied to the power operator the decomposition in eigenvalues and eigenvectors, becoming possible to compute the numerical equivalent to the supersonic intensity, called here useful intensity, after applying a cutoff criterion to remove the non propagating components. Some numerical tests confirming the effectiveness of the convergence criterions are presented. Examples of the application of the useful intensity technique in vibrating surfaces such as a plate, a cylinder with flat caps and an automotive muffler are presented and the numerical results are discussed, showing that the useful intensity brings, as additional benefit, a reduction of the computational effort, when compared to existent numerical technique.

At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.

The vast and rich body of literature covering the numerical modelling of hydrodynamic floating body systems has demonstrated their great power and versatility when applied to offshore marine energy systems. It is possible to model almost any type of physical phenomenon which could be expected within such a system, however, limitations of computing power continue to restrict the usage of the most comprehensive models to very narrow and focused design applications. Despite the continued evolution of parallel computing, one major issue that users of computational tools invariably face is how to simplify their modelled systems in order to achieve practically the necessary computations, whilst capturing enough of the pertinent physics, with great enough ‘resolution’, to give robust results. The challenge is, in particular, to accurately deliver a complete spectrum of results, that account for all of the anticipated sea conditions and allow for the optimisation of different control scenarios. This thesis examines the uncertainty associated with the effects of viscosity and nonlinear behaviour on a small scale model of an oscillating system. There are a wide range of Computational Fluid Dynamics (CFD) methods which capture viscous effects. In general however, the oscillating, six degree-of-freedom floating body problem is best approached using a linear potential flow based Boundary Element Method (BEM), as the time taken to process an equivalent model will differ by several orders of magnitude. For modelling control scenarios and investigating the effects of different sea states, CFD is highly impractical. As potential flows are inviscid by definition, it is therefore important to know how much of an impact viscosity has on the solution, particularly when different scales are of interest during device development. The first aim was to develop verified and validated solutions for a generic type decaying system. The arrangement studied was adapted from an array tank test experiment which was undertaken in 2013 by an external consortium (Stratigaki et al., 2014). Solutions were delivered for various configurations and gave relatively close approximations of the experimental measurements, with the modelling uncertainties attributed to transient nonlinear effects and to dissipative effects. It was not possible however to discern the independent damping processes. A set of CFD models was then developed in order to investigate the above discrepancies, by numerically capturing the nonlinear effects, and the effects of viscosity. The uncontrolled mechanical effects of the experiment could then be deduced by elimination, using known response patterns from the measurements and derived results from the CFD simulations. The numerical uncertainty however posed a significant challenge, with the outcomes supported by verification evidence, and detailed discussions relating to the model configuration. Finally, the impact of viscous and nonlinear effects were examined for two different interacting systems – for two neighbouring devices, and an in-line array of five devices. The importance of interaction behaviour was tested by considering the transfer of radiation forces between the model wave energy converters, due to the widely accepted notion that array effects can impact on energy production yields. As there are only very limited examples of multi-body interaction analysis of wave energy devices using CFD, the results with this work provide important evidence to substantiate the use of CFD for power production evaluations of wave energy arrays. An effective methodology has been outlined in this thesis for delivering specific tests to examine the effects of viscosity and nonlinear processes on a particular shape of floating device. By evaluating both the inviscid and viscous solutions using a nonlinear model, the extraction of systematic mechanical effects from experimental measurements can be achieved. As these uncontrolled frictional effects can be related to the device motion in a relatively straightforward manner, they can be accommodated within efficient potential flow model, even if it transpires that they are nonlinear. The viscous effects are more complex; however, by decomposing into shear and pressure components, it may in some situations be possible to capture partially the dynamics as a further damping term in the efficient time-domain type solver. This is an area of further work.

Cette thèse a consisté à élaborer une méthode qui permet de résoudre l’équation intégrale comportant comme inconnues les courants et les charges introduite récemment par Taskinen et Ylä-Oijala par une méthode d’éléments frontière sans aucune contrainte de continuité au niveau des interfaces des éléments aussi bien pour les courants que pour les charges. Nous avons d’abord montré comment on pouvait construire cette équation de façon simple et similaire à celle des formulations intégrales usuelles en imposant au problème intérieur relatif au système de Picard, qui est en fait une extension du système de Maxwell, des conditions aux limites adéquates. Pour des géométries régulières de l’objet diffractant, nous avons établi de façon théorique la stabilité et la convergence des schémas numériques ci-dessus en montrant que cette équation peut être décomposée sous la forme d’un système elliptique coercif et d’un opérateur compact dans le cadre des fonctions de carré intégrable.Toute cette étude a été confirmée par des tests numériques tridimensionnels. Comme pour les équations intégrales usuelles de seconde espèce, le cadre théorique valable pour des surfaces régulières ne l’est plus pour des surfaces avec des singularités. L’utilisation formelle de cette équation,pour des surfaces singulières, a donné des résultats entachés d’erreur. Nous avons mis en évidence l’origine des instabilités numériques à l’origine de ces erreurs lorsque les géométries sont singulières en développant une version bidimensionnelle de cette équation. Cette version nous a permis en particulier de montrer que les instabilités étaient dues à des oscillations parasites concentrées autour des singularités de la géométrie. Dans ce cadre nous avons pu mettre en oeuvre plus aisément des approches pour supprimer ou atténuer ces oscillations parasites ou leur effet sur les calculs en champ lointain. Nous avons montré qu’un procédé d’augmentation des degrés de liberté pour la charge par rapport au courant pouvait sensiblement réduire ces instabilités. A la suite de l’amélioration observée sur les résultats dans le cas 2D, nous avons transposé cette procédure au cas tridimensionnel. A travers divers tests, nous avons constaté l’amélioration de la qualité de l’approximation amenée par la procédure de stabilisation / The objective of this thesis was to develop a method that solves the integral equation whose unknowns are the currents and the charges, recently introduced by Taskinen and Ylä-Oijala, by a boundary element method without any continuity constraint at the interfaces of the elements,for both the unknowns. We first show how to construct this equation in a simple way, similar tothe usual integral formulations, through imposing to the internal problem related to the Picard system,which is an extension of the Maxwell system, appropriate boundary conditions. For regular geometries, we have established a theoretical background ensuring the stability and the convergence of numerical scheme, by proving that this equation can be decomposed in a coercive elliptic and a compact parts in the context of square integrable functions. Our study was validated by three-dimensional numerical tests. In the case of usual integral equations of the second kind, the theoretical background for smooth surfaces is no longer valid when the surfaces is singular. The formal use of this equation for singular surfaces gave erroneous results. We pointed out the origin of numerical instabilities bydeveloping a two-dimensional version of this equation. This version has allowed us to show that the instabilities were due to parasitic oscillations accumulating on the geometrical singularities. In this context, we have implemented some approaches to reduce this parasitic oscillations on the calculations in the far field.We have shown that the method of increasing the freedom degrees for the charges relatively to the current could significantly reduces these instabilities. As a result, we have implemented this procedure in three-dimensional case. Throughout various tests, we noted the improvement on the approximation brough bay to the stabilization procedure