Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2015-03-27T12:06:51Z No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-03-27T15:28:00Z (GMT) No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-03-27T15:28:00Z (GMT). No. of bitstreams: 2 Dissertação - Vitor Escher Martins - 2014.pdf: 13588446 bytes, checksum: 9cceb42b5d24095bc392dc37f17c9386 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-06-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Over the years, fiber-reinforced composite laminated shells have been widely used as structural components in several engineering areas and industrial applications. These structures can been subjected to extreme working conditions, either by a fluid structure interaction or even by both dynamic external load and thermal load that provides additional compressive stresses acting along the shell. In the present work, the nonlinear dynamic behavior and stability of fluid-filled laminated cylindrical shells under both thermal and lateral loads is investigated. To model the shell the nonlinear Amabili-Reddy Higher-Order Shear Deformation Theory is applied, the hydrodynamic pressure of the fluid is model by the potential flow theory and a linear temperature distribution is proposed along the thickness of the shells. Classical shells theories, which neglect shear deformation and rotary inertia, give inaccurate analysis results for moderately thick laminated shells. Due to this limitation, higher-order shear deformation theories can represent better the kinematics behavior and can yield more accurate interlaminar stress.To discretize the shell a 23 d.o.f. displacement field is used containing the axial, circumferential, lateral displacements, rotations as well as the coefficients to consider the shear effect. The Ritz method is applied in order to obtain a set of nonlinear ordinary differential equations of motions, which are in turn solved by the Runge-Kutta method. The obtained resonance curves and bifurcation diagrams show the great influence of both laminated material and the temperature on the nonlinear behavior of the shells. / Ao longo dos anos cascas cilíndricas laminadas reforçadas com fibras têm sido amplamente utilizadas como componentes estruturais em diversas áreas da engenharia e aplicações industriais. Durante sua vida operacional, essas estruturas são constantemente submetidas às extremas condições de trabalho, seja em função da interação fluido- estrutura, cargas externas dinâmicas ou mesmo por cargas térmicas que produzem tensões adicionais de compressão sobre a superfície da casca. Neste trabalho será investigado o comportamento dinâmico não linear de cascas cilíndricas laminadas com a presença de um meio fluido em repouso no interior da casca, além de se estudar a influência de esforços laterais dinâmicos solicitantes, juntamente com a variações de temperatura. A teoria de Amabili-Reddy de deformação por cisalhamento de ordem superior é utilizada para modelar o comportamento mecânico dos esforços e deformações da casca, garantindo assim, uma melhor distribuição das tensões interlaminares, ou seja, ao longo de sua direção radial. A análise é realizada para cascas simplesmente apoiadas, em que são consideradas três expansões de deslocamento, respectivamente nas direções longitudinal, circunferencial e radial, além de duas expansões para as rotações da linha neutra nos planos xz z, discretizando o problema em 23 graus de liberdade. O método de Ritz é aplicado para a obtenção do sistema de equações de movimento não linear (EDO), além do método de Runge-Kutta de 4º Ordem e o método de Força Bruta que são utilizados para se investigar o comportamento dinâmico das análises em questão.

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Wave propagation is a phenomenon resulting from high transient loadings where the duration of the load is in µ seconds range. In aerospace and space craft industries it is important to gain knowledge about the high frequency characteristics as it aids in structural health monitoring, wave transmission/attenuation for vibration and noise level reduction. The wave propagation problem can be approached by the conventional Finite Element Method(FEM); but at higher frequencies, the wavelengths being small, the size of the finite element is reduced to capture the response behavior accurately and thus increasing the number of equations to be solved, leading to high computational costs. On the other hand such problems are handled in the frequency domain using Fourier transforms and one such method is the Spectral Finite Element Method(SFEM). This method is introduced first by Doyle ,for isotropic case and later popularized in developing specific purpose elements for structural diagnostics for inhomogeneous materials, by Gopalakrishnan. The general approach in this method is that the partial differential wave equations are reduced to a set of ordinary differential equations(ODEs) by transforming these equations to another space(transformed domain, say Fourier domain). The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equations and hence, the exact elemental dynamic stiffness matrix is derived. Thus, in the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FEM, but in the transformed space. Thus after obtaining the solution, the original domain responses are obtained using the inverse transform. Both the above mentioned manuscripts present the Fourier transform based spectral finite element (FSFE), which has the inherent aliasing problem that is persistent in the application of the Fourier series/Fourier transforms. This is alleviated by using an additional throw-off element and/or introducing slight damping in to the system. More recently wave let transform based spectral finite element(WSFE) has been formulated which alleviated the aliasing problem; but has a limitation in obtaining the frequency characteristics, like the group speeds are accurate only up-to certain fraction of the Nyquist(central frequency). Currently in this thesis Laplace transform based spectral finite elements(LSFE) are developed for sandwich members. The advantages and limitations of the use of different transforms in the spectral finite element framework is presented in detail in Chapter-1. Sandwich structures are used in the space craft industry due to higher stiffness to weight ratio. Many issues considered in the design and analysis of sandwich structures are discussed in the well known books(by Zenkert, Beitzer). Typically the main load bearing structures are modeled as beam sand plates. Plate structures with kh<1 is analysed based on the Kirch off plate theory/Classical Plate Theory(CPT) and when the bending wavelength is small compared to the plate thickness, the effect of shear deformation and rotary inertia needs to be included where, k is the wave number and h is the thickness of the plate. Many works regarding the wave propagation in sandwich structures has been published in the past literature for wave propagation in infinite sandwich structure and giving the complete description of dispersion relation with no restriction on frequency and wavelength. More recently exact analytical solution or simply supported sandwich plate has been derived. Also it is seen by comparison of dispersion curves obtained with exact (3D formulation of theory of elasticity) and simplified theories (2D formulation as generalization of Timoshenko theory) made on infinite domain and concluded that the simplified theory can be reliably used to assess the waveguide properties of sandwich plate in the frequency range of interest. In order to approach the problems with finite domain and their implementation in the use of general purpose code; finite degrees of freedom is enforced. The concept of displacement based theories provides the flexibility in assuming different kinematic deformations to approach these problems. Many of the displacement based theories incorporate the Equivalent Single Layer(ESL) approach and these can capture the global behavior with relative ease. Chapter-2 presents the Laplace spectral finite element for thick beams based on the First order Shear Deformation Theory (FSDT). Here the effect of different choices of the real part of the Laplace variable is demonstrated. It is shown that the real part of the Laplace variable acts as a numerical damping factor. The spectrum and dispersion relations are obtained and the use of these relations are demonstrated by an example. Here, for sandwich members based on FSDT, an appropriate choice of the correction factor ,which arises due to the inconsistency between the kinematic hypothesis and the desired accuracy is presented. Finally the response obtained by the use of the element is validated with experimental results. For high shock loading cases, the core flexibility induces local effects which are very predominant and this can lead to debonding of face sheets. The ESL theories mentioned above cannot capture these effects due to the computation of equivalent through the thickness section properties. Thus, higher order theories such as the layer-wise theories are required to capture the local behaviour. One such theory for sandwich panels is the Higher order Sandwich Plate theory (HSaPT). Here, the in-plane stress in the core has been neglected; but gives a good approximation for sandwich construction with soft cores. Including the axial inertial terms of the core will not yield constant shear stress distribution through the height of the core and hence more recently the Extended Higher order Sandwich Plate theory (EHSaPT) is proposed. The LSFE based on this theory has been formulated and is presented in Chapter-4. Detailed 3D orthotropic properties of typical sandwich construction is considered and the core compressibility effect of local behavior due to high shock loading is clearly brought out. As detailed local behavior is sought the degrees of freedom per element is high and the specific need for such theory as compared with the ESL theories is discussed. Chapter-4 presents the spectral finite element for plates based on FSDT. Here, multi-transform method is used to solve the partial differential equations of the plate. The effect of shear deformation is brought out in the spectrum and dispersion relations plots. Response results obtained by the formulated element is compared and validated with many different experimental results. Generally structures are built-up by connecting many different sub-structures. These connecting members, called joints play a very important role in the wave transmission/attenuation. Usually these joints are modeled as rigid joints; but in reality these are flexible and exhibits non-linear characteristics and offer high damping to the energy flow in the connected structures. Chapter-5 presents the attenuation and transmission of wave energy using the power flow approach for rigid joints for different configurations. Later, flexible spectral joint model is developed and the transmission/attenuation across the flexible joints is studied. The thesis ends with conclusion and highlighting futures cope based on the developments reported in this thesis.