No description available.

No description available.

<p>The aerodynamic excitation of the diametral acoustic modes of an axisymmetric cavity-duct system is investigated experimentally. The change experienced by the acoustic diametral modes with the increase of the mean flow Mach number is investigated numerically. The first objective of this research is to examine the ability of the axisymmetric free shear layer forming along the cavity mouth to excite the asymmetric diametral modes which do not have preferred azimuthal orientations. The dependency of the system aeroacoustic response on both the cavity length and its depth is investigated to determine the limitations imposed by the relative dimensions of the cavity on the excitation process. The azimuthal behaviour of the self-excited diametral modes is also characterized.</p> <p> An experimental set-up is designed to ensure the coincidence of the frequencies of the shear layer oscillation with the acoustic resonance frequencies. The selection of the test section dimensions is based on finite element simulation of the acoustic diametral modes for several geometries. To simulate the diametral modes at different flow Mach numbers, a finite difference code is developed based on a two-step computational aeroacoustic approach. This approach allows the simulation of the acoustic field, taking into account the convection effect of the mean flow.</p> <p>The experimental results show that the diametral modes are very liable to be self-excited when the mean flow Mach number is higher than 0.1. The level of acoustic pressure during the diametral mode resonance increases rapidly with the increase of the ratio of the cavity depth, d, to the pipe diameter, D. However, the maximum acoustic pressure during each resonance decreases with the increase of the ratio of the cavity length, L, to the pipe diameter, D. The selfexcitation of the diametral modes is sustainable with d/D as small as 1/12. Further reduction in this ratio may result in complete suppression of the resonance. For deep cavities, d/D>3/12, the first and second diametral modes are more liable to excitation than the higher order modes. This is attributed to the fact that the low order modes have relatively higher radial acoustic particle velocity amplitude at the cavity mouth compared to the higher order ones. For d/D=l/12, the higher order modes have relatively higher radial acoustic particle velocity amplitude and consequently their tendency to be self-excited increases. For long cavities, L/D>2/3, the duct longitudinal acoustic modes start to be excited and become more dominant as the cavity length is further increased. The excitation mechanism of these longitudinal modes has not been investigated in this work since sufficient details already exist in the literature.</p> <p>The azimuthal behaviour of the diametral modes is characterized for all the tested cases. For short cavities, the diametral modes are classified as spinning modes; while for long cavities, L/D> 1/2, the orientation of the mode changes randomly over time. Small imperfections in the axisymmetric geometry result in what is described as partially spinning modes. An analytical model is developed to describe quantitatively the spinning behaviour of the diametral modes. The free shear layer and the diametral modes are found to be fully coupled in the azimuthal direction. The random behaviour of the diametral modes in the case of long cavities is attributed to the increase of randomness in the turbulent shear layer </p> <p>The numerical simulations show that the diametral modes experience considerable changes with the increase of the mean flow Mach number. At the cavity mouth, both the amplitude and phase distributions of the acoustic particle velocity are altered with the increase of the Mach number. This demonstrates the importance of considering the effect of the mean flow on the acoustic power production process. Moreover, the resonance frequency of the diametral modes decreases with the increase of the Mach number.</p> / Thesis / Doctor of Philosophy (PhD)

The flow of jets in confining enclosures has significant application in many engineering processes. In particular, two jet flows have been studied; the impingement of axisymmetric jets in a confined space and a turbulent inlet wall jet in a confining enclosure. The impingement of axisymmetric jets in a cavity has been examined using flow visualization, laser Doppler anemometry, and numerical simulations. When the flow field was examined under various geometrical and fluid parameters several flow regions were found, depending on the geometrical and fluid parameters. Initially, a steady flow field existed for all arrangements for Red < ~90 but subsequent increments in the fluid velocity caused an oscillating flow field to emerge. The onset of the oscillations and the upper limit of finite oscillations were found to be a function of the nozzle diameter to chamber dimension ratio. Although steady numerical simulations predicted the steady flow field well, steady simulations of the oscillating flow field over-predicted the peak axial velocities. The oscillating flow field is considered to be a class of self-sustaining oscillations where instabilities in the jet shear layer are amplified because of feed back from pressure disturbances in the impingement region. The turbulent wall jet in a cavity has been studied using flow visualization, laser Doppler anemometry (LDA), particle streak velocimetry (PSV) and numerical simulations. Instantaneous PSV measurements agreed well with time averaged LDA measurements. Two dimensional simulations using an algebraic stress turbulence model (ASM) were in better agreement with the experimental data than two and three dimensional simulations using a k - ε turbulence model in the wall jet region. A wall jet growth rate was found to be 54% higher than a wall jet in stagnant surroundings due to the enclosure boundaries. / Thesis / Doctor of Philosophy (PhD)

Axisymmetric analysis of cylindrical contacts is considered in the context of axisymmetric assemblies such as shrink-fits. Fretting fatigue induces sub-critical cracks along the contact interface of press fits especially when they are subjected to vibration. The surface and near surface stresses play a major role in the fretting fatigue crack initiation process. Assuming near surface contact stresses to be largely independent of the actual geometry of components in contact, half-plane analyses and experimental results obtained from a strip configuration are often cited in the literature to predict and understand crack initiation in the actual components (ASTM STP 1425). This thesis starts with half plane and strip models for cylindrical contact such as in a shrink fitted shaft. Different traction profiles underpinning a typical fretting contact constitute a study of different geometrical parameters and friction coefficients. The cylindrical shrink fitted contact is considered using mixed boundary formulation. The different cases of contact such as full slip, partial stick-slip and full stick are considered. A formulation for cyclically varying tractions is attempted using dynamic elasticity. Finally, the problem of cylindrical cracks is highlighted to understand interface delamination in a fiber reinforced composite. Stress functions in conjunction with Fourier transforms are used for analysis. Dynamic potentials based on Helmholtz decomposition are used for dynamic loading.For static loading Love’s stress function is used for axisymmetric problems while Airy’s stress function is used for 2D problems. Solution procedures for solving traction boundary and mixed boundary conditions are described. Preliminary experiments are described to appreciate the contact stresses and crack initiation in cylindrical contact. Photoelastic fringes in a cylinder under a band of pressure illustrate fretting contact stresses concentrated close to the surface with the core of the cylinder relatively unstressed. Further, some material testing experiments using a specially designed cylindrical fretting rig demonstrated typical features of fretting fatigue crack initiation for providing the theoretical motivation. Fretting fatigue induces the initiation of a number of sub critical cracks along the contact interface of components in mechanical assemblies especially under vibration. The dominant crack among the initiated cracks may grow in size to the critical length in the presence of bulk cyclic loading finally resulting in fracture of the entire component. Fretting fatigue leads to unexpected failure of the component well below the expected life. It is therefore, critical to analyse, detect and control fretting. The blade root-disk joint in gas turbines as a critical example of fretting fatigue has spurred extensive research effort. There is relatively little literature available on cylindrical fretting in shrink fitted joint focused in this thesis. Analytical solutions for static fretting tractions are presented using both axisymmetric and plane elastic stress functions for later comparison. While Fourier transforms in conjunction with Airys stress functions are exploited for attacking plane problems, Loves axisymmetric stress functions are explored for cylindrical fretting. Near surface stresses are of great interest in fretting fatigue research. Although two dimensional models provide general understanding of stresses caused during fretting, these models become inadequate to explain the interaction of local stresses with the bulk stresses inevitably present in cylindrical components. Global stress analysis tools are desirable for estimating the fatigue life of components experiencing fretting. While numerical techniques immensely aid fatigue life estimation they have their limitation when it comes to coated components. Stress analysis of coated cylinders unveils the intricate influence of the elastic mismatch as well as the width of the loading for varying friction coefficients. Comparison of results obtained from axisymmetric elasticity with plane elasticity is discussed in detail. The validity and scope of relying on plane fretting results to cylindrical fretting contacts is examined by comparing the results obtained for three different traction profiles. Fretting is generally modeled as a stress boundary value problem wherein the normal and frictional shear stresses are prescribed on the cylindrical surface. In reality fretting generally turns out to be a mixed boundary value problem with unknown regions of stick and slip requiring prescribing traction and displacement simultaneously. This belongs to a formidable class of unsolved contact mechanics problems in cylindrical axisymmetric elasticity. The famous spherical axisymmetric Hertz problem has no cylindrical counterpart except in the limiting case of a cylinder of large radius. These aspects are investigated for studying the hub-shaft interfacial geometry. A conformal contact profile is considered to model a shrink fit; the contact pressure is zero at the ends of contact. The case of full slip condition is analysed assuming a frictionless contact. With friction, partial stick-slip condition is analysed. The unknown contact traction is resolved in terms of Chebyshev expansions whose unknown coefficients are solved using Schmidt method. The unknown contact length and stick zone length are determined through an iterative procedure. A rigid uneven undulating axisymmetric hub in total contact over an elastic shaft under full stick condition is analysed for obtaining the near surface stresses for a given value of hub penetration. Even though the stresses oscillate in fretting, almost all the analyses reported in the literature use static formulation. Understanding this need, a dynamic analysis for modeling fretting of a cylinder subjected to harmonic pressure and shear is attempted. The Pochhammer dispersion relation becomes a prerequisite for a dynamic analysis. The results show that the stresses do not decay away from the contact, in contrast to the static results. This shows the propagation of stresses along the axial direction. Further extension of the dynamic analysis to a layered cylinder is also described. The results obtained on contact stresses and contact tractions under the cylindrical contact represent a significant advance to the literature for modeling fretting fatigue crack initiation and propagation. Formulating cylindrical crack problems is somewhat similar to cylindrical contacts. Such cylindrical cracks arise from the debonding along the fiber-matrix interface of a composite. A unified formulation for the problem of a pressurised cylindrical crack as also a pair of 2D parallel cracks in infinite media is attempted using Love’s stress function in conjunction with Fourier transforms. The results obtained for stress intensity factors, strain energy release rate, mode mixity, crack opening and sliding displacements are compared with that of a 2D pair of parallel cracks obtained using the unified formulation. The asymptotic situation of a large crack length to spacing ratio is examined in detail. In the case of a pair of parallel cracks, this implies a single crack in mode-I as far as the total energy release rate is concerned while at the same time retaining an asymptotic value for the mode mixity. This unique feature of near field mixed mode blending smoothly to mode-I in the far field is also seen for the stress field around a symmetrically branched crack. Thus, this thesis presents a collection of cylindrical elastostatic and elastodynamic axisymmetric solutions to provide better understanding of fretting and delamination problems encountered in press fit assemblies.

No description available.

The automotive industry is currently trying to replace the conventional steels to lightweight materials such as aluminum or carbon fiber to meet all stricter emission targets. When using such materials, traditional joining methods, such as spot welds, could be difficult to use. Therefore, more focus has been put on self-piercing rivets (SPR).In whole car models used in crash simulations, substitution models are used to model SPR joints. It is important to calibrate these models for different load cases. Volvo Cars Corporation (VCC) are currently calibrating using time-consuming physical tests where the SPR joint is subjected to loads in different directions. To save time, a way of virtually evaluating the SPR joint strength is therefore sought after. To do this, a method was developed using non-linear FEM in LS-DYNA. The method was then used to perform sensitivity studies concerning friction, sheet thickness and rivet geometry.The method developed can be divided into three parts. The process simulation, where the rivet insertion was simulated. A springback analysis, where the material is allowed to springback, closer resembling the real behaviour. Finally, the three destructive tests, lap-shear, cross-tension and KS2, were built using the geometry and initial values from the springback.For the process simulation, an explicit solution was used. To handle the large deformations present during the event, r-adaptivity was used together with a kill-element-method to describe failure, based on CrachFEM or Gissmo. The following springback analysis was then performed using one implicit step.For the destructive tests, a solid element representation of the SPR joint was created using the geometry and initial values from the springback. A shell-solid hybrid model was used to keep the computational time low.Using the method, a good correlation was found both for the process- and the destructive test simulations when compared to experiments. Furthermore, it could be concluded that friction, sheet thickness and rivet geometry affects the SPR joint strength and characteristics.

The objective of the dissertation is to develop and describe kinematic models (Pseudo-Rigid-Body Models) for approximating large-deflection of spatial (3D) cantilever beams that undergo multiple bending motions thru end-moment loading. Those models enable efficient design of compliant mechanisms, because they simply and accurately represent the bending and stiffness of compliant beams. To accomplish this goal, the approach can be divided into three stages: development of the governing equations of a flexible cantilever beam, development of a PRBM for axisymmetric cantilever beams and the development of spatial PRBMs for rectangular cross-section beam with multiple end moments. The governing equations of a cantilever beam that undergoes large deflection due to force and moment loading, contains the curvature, location and rotation of the beam. The results where validated with Ansys, which showed to have a Pearson's correlation factor higher than 0.91. The resulting deflections, curvatures and angles were used to develop a spatial pseudo-rigid-body model for the cantilever beam. The spatial pseudo-rigid-body model consists of two links connected thru a spherical joint. For an axisymmetric beam, the PRB parameters are comparable with existing planar PRBMs. For the rectangular PRBM, the parameters depend on the aspect ratio of the beam (the ratio of the beam width over the height of the cross-section). Tables with the parameters as a function of the aspect ratio are included in this work.

[pt] O emprego de materiais compósitos em estruturas tem ganhado importância na prática da engenharia devido às suas características de alta resistência mecânica, baixa densidade e boa estabilidade a efeitos térmicos. Uma das classes de compósitos, a de laminados fibrosos, pode ser utilizada em tubulações sujeitas às diversas formas de carregamentos, como pressão interna e/ou externa, tração longitudinal, torção, temperatura, etc. O presente Trabalho tem por objetivo propor, implementar e testar a formulação de um modelo de elemento finito axissimétrico, para a representação do comportamento de um tubo laminado por camadas de materiais compósitos fibrosos. A modelagem consiste em representar a seção geratriz de um tubo cilíndrico por um elemento quadrilateral de quatro nós, com três graus de liberdade por nó, com os deslocamentos nodais tomados em relação aos eixos de um sistema cilíndrico de coordenadas. Considera-se a perfeita adesão das camadas, garantindo a continuidade do campo de deslocamentos. Modelos constitutivos de materiais com o comportamento ortotrópico e/ou o transversalmente isotrópico foram implementados, obtendo-se respostas para os campos de deslocamentos, de deformações e de tensões atuantes. Na validação do modelo numérico, considerou-se a comparação de seus resultados com os de soluções analíticas, disponíveis na literatura, e aqueles fornecidos por um programa comercial de elementos finitos, empregando o modelo com elementos sólidos. Foram propostos, para os testes em ambos os casos, exemplos de laminados com uma a quatro camadas, com fibras orientadas em diferentes ângulos. Destas comparações, verifica-se uma boa convergência das soluções numéricas obtidas com o presente modelo, representativo das principais características cinemáticas da classe de problemas representada. / [en] The use of composite materials in structures has grown in the engineering practice due to its characteristics, of high strength, low density and a good stability to thermal effects. A class of composites, the fibrous laminates, is generally used in tubes subjected to many types of loadings as internal and/or external pressure, traction, torsion, temperatures, etc. This work has the objectives to propose, implement and test an axisymmetric finite element model formulation that represents the mechanical behavior of a fibrous laminated composite tube. Modeling consists in representing the cylindrical tube generating section by a quadrilateral element with four nodes and three degrees-of-freedom per node, with three nodal displacements defined in a cylindrical coordinate system. Layers are considered perfectly bonded together, assuring continuity between elements on the displacement fields. Orthotropic and/or transverse isotropic constitutive material models were implemented, allowing solutions for displacement, strain and stress fields. In the element numerical model validation, result comparisons with those from analytical solutions available on literature and those from the use of layered solid elements in a commercial finite element program were considered. Some examples, considering one to four layers, with different fiber angles, were proposed for model testing. It is noted a good numerical convergence for the presenting model solutions which represent the main kinematic characteristics for this class of problems.

This work is concerned with the Almost Axisymmetric Flows with Forcing Terms which are derived from the inviscid Boussinesq equations. It is our hope that these flows will be useful in Meteorology to describe tropical cyclones. We show that these flows give rise to a collection of Monge-Ampere equations for which we prove an existence and uniqueness result. What makes these equations unusual is the boundary conditions they are expected to satisfy and the fact that the boundary is part of the unknown. Our study allows us to make inferences in a toy Almost Axisymmetric Flows with a forcing term model.