Pontes são estruturas denominadas obras de arte ou obras especiais, utilizadas em rotas e vias de comunicação, possibilitando que veículos atravessem obstáculos naturais ou artificiais como, por exemplo, rios. Tais estruturas são calculadas e construídas considerando os esforços aos quais serão submetidas em serviço e sua distribuição na estrutura. Além disso, também existe a necessidade de se avaliar as frequências naturais de vibração para garantir a segurança das mesmas. No presente trabalho são analisados alguns problemas relacionados às vibrações de pontes e viadutos em grelha, resultantes das variações de rigidez e massa nessas estruturas. Essa análise foi feita considerando-se que vibrações excessivas não condizem com o conforto humano e durabilidade da ponte. Ademais, para a estrutura é interessante fugir do efeito de ressonância, que acontece quando a frequência de excitação coincide com uma das frequências naturais de oscilação do sistema. Essa condição faz o sistema vibrar em amplitudes cada vez maiores, podendo causar inclusive a ruína. Para estudar formas de sair de uma frequência natural não amortecida indesejada, foi realizada uma pesquisa paramétrica das características dinâmicas deste tipo de estrutura, modificando parâmetros como rigidez (pela distribuição de longarinas e de transversinas), massa (devido à alteração das dimensões) e danos estruturais causados durante a vida útil da estrutura. Com intuito de estudar diversos modelos, foram adotadas três diferentes situações de projeto: superestrutura com variadas alturas de longarinas e transversinas, da qual foi possível concluir que a altura da longarina tem mais impacto na frequência natural não amortecida da estrutura que a transversina; pequenos defeitos ou danos na estrutura e o efeito de uma longarina rompida para os quais foram comparadas suas frequências naturais não amortecidas. As análises foram realizadas pelo Método dos Elementos Finitos, utilizando-se o programa comercial SAP2000. / Bridges are structures sometimes referred as works of art or special works, used on routes and roads that allow vehicles to cross natural or artificial obstacles, such as rivers. Such structures are calculated and constructed considering the efforts to which they will be submitted in service and their distribution in the structure. In addition, there is also a need to evaluate the natural frequencies of vibration to ensure their safety. In the present study some effects were analyzed related to the vibrations of grid bridges and viaducts resulting from changes in stiffness and mass in these structures. This analysis was made considering that excessive vibrations are not consistent with human comfort and bridge durability. For the structure, it is interesting to stay away from the resonance effect, which occurs when the excitation frequency matches one of the natural frequencies of oscillation of the system. This leads to oscillation with increasing amplitudes which may cause even the ruin. In order to study several models, three different design situations were adopted: superstructure with varying heights of beams and crossbeams, from which it was possible to conclude that the height of the beams has more impact on the undamped natural frequency of the structure than the crossbeams; small defects or damage to the structure and the effect of a ruptured beam for which its undamped natural frequencies were compared. The analysis were performed using the Finite Element Method, using the SAP2000 commercial program.

Pontes são estruturas denominadas obras de arte ou obras especiais, utilizadas em rotas e vias de comunicação, possibilitando que veículos atravessem obstáculos naturais ou artificiais como, por exemplo, rios. Tais estruturas são calculadas e construídas considerando os esforços aos quais serão submetidas em serviço e sua distribuição na estrutura. Além disso, também existe a necessidade de se avaliar as frequências naturais de vibração para garantir a segurança das mesmas. No presente trabalho são analisados alguns problemas relacionados às vibrações de pontes e viadutos em grelha, resultantes das variações de rigidez e massa nessas estruturas. Essa análise foi feita considerando-se que vibrações excessivas não condizem com o conforto humano e durabilidade da ponte. Ademais, para a estrutura é interessante fugir do efeito de ressonância, que acontece quando a frequência de excitação coincide com uma das frequências naturais de oscilação do sistema. Essa condição faz o sistema vibrar em amplitudes cada vez maiores, podendo causar inclusive a ruína. Para estudar formas de sair de uma frequência natural não amortecida indesejada, foi realizada uma pesquisa paramétrica das características dinâmicas deste tipo de estrutura, modificando parâmetros como rigidez (pela distribuição de longarinas e de transversinas), massa (devido à alteração das dimensões) e danos estruturais causados durante a vida útil da estrutura. Com intuito de estudar diversos modelos, foram adotadas três diferentes situações de projeto: superestrutura com variadas alturas de longarinas e transversinas, da qual foi possível concluir que a altura da longarina tem mais impacto na frequência natural não amortecida da estrutura que a transversina; pequenos defeitos ou danos na estrutura e o efeito de uma longarina rompida para os quais foram comparadas suas frequências naturais não amortecidas. As análises foram realizadas pelo Método dos Elementos Finitos, utilizando-se o programa comercial SAP2000. / Bridges are structures sometimes referred as works of art or special works, used on routes and roads that allow vehicles to cross natural or artificial obstacles, such as rivers. Such structures are calculated and constructed considering the efforts to which they will be submitted in service and their distribution in the structure. In addition, there is also a need to evaluate the natural frequencies of vibration to ensure their safety. In the present study some effects were analyzed related to the vibrations of grid bridges and viaducts resulting from changes in stiffness and mass in these structures. This analysis was made considering that excessive vibrations are not consistent with human comfort and bridge durability. For the structure, it is interesting to stay away from the resonance effect, which occurs when the excitation frequency matches one of the natural frequencies of oscillation of the system. This leads to oscillation with increasing amplitudes which may cause even the ruin. In order to study several models, three different design situations were adopted: superstructure with varying heights of beams and crossbeams, from which it was possible to conclude that the height of the beams has more impact on the undamped natural frequency of the structure than the crossbeams; small defects or damage to the structure and the effect of a ruptured beam for which its undamped natural frequencies were compared. The analysis were performed using the Finite Element Method, using the SAP2000 commercial program.

This thesis investigates the implementation of a passive isolator with a pressurized air cushion for spacecraft payloads in mission architectures implementing in-space assembly technologies. A pressurized air bed capable of briefly surviving the space environment for cargo delivery was prototyped and experimentally evaluated for launch vehicle vibration dynamics resulting in a 72%, 93%, and 88% reduction in experienced GRMS loads for the X-Axis, Y-Axis, and Z-Axis, respectively. A preliminary Total Mass Loss evaluation of the Low-Density Polyethylene Film utilized for the air bed resulted in a mass loss of 0.7%, indicating that commercial off-the-shelf films might require minimal modification for flight readiness. An analytical model of a planar rectangular payload experiencing free vibrations with a Winkler foundation is generated and compared to the experimental results, showing a potential way for characterizing and designing such a foundation to reduce experienced vibrations. These preliminary results show a potential path for a non-cost-prohibitive method for space payloads to reduce loads experienced during launch as inspired by the successful hosted payloads program aboard the International Space Station.

In this study, Ritz method has been employed to analyze the following problems: free vibrations of plates with curvilinear stiffeners, the lowest 100 frequencies of thick isotropic plates, free vibrations of thick quadrilateral laminates and free vibrations and static deformations of rectangular laminates, and sandwich structures. Admissible functions in the Ritz method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made possible by additive manufacturing, both plate and stiffeners are modeled using a first-order shear deformation theory. For the thick isotropic plates and laminates, a third-order shear and normal deformation theory is used. The accuracy and computational efficiency of formulations are shown through a range of numerical examples involving different boundary conditions and plate thicknesses. The above formulations assume the whole plate as an equivalent single layer. When the material properties of individual layers are close to each other or thickness of the plate is small compared to other dimensions, the equivalent single layer plate (ESL) theories provide accurate solutions for vibrations and static deformations of multilayered structures. If, however, sufficiently large differences in material properties of individual layers such as those in sandwich structure that consists of stiff outer face sheets (e.g., carbon fiber-reinforced epoxy composite) and soft core (e.g., foam) exist, multilayered structures may exhibit complex kinematic behaviors. Hence, in such case, C_z⁰ conditions, namely, piecewise continuity of displacements and the interlaminar continuity of transverse stresses must be taken into account. Here, Ritz formulations are extended for ESL and layerwise (LW) Nth-order shear and normal deformation theories to model sandwich structures with various face-to-core stiffness ratios. In the LW theory, the C⁰ continuity of displacements is satisfied. However, the continuity of transverse stresses is not satisfied in both ESL and LW theories leading to inaccurate transverse stresses. This shortcoming is remedied by using a one-step well-known stress recovery scheme (SRS). Furthermore, analytical solutions of three-dimensional linear elasticity theory for vibrations and static deformations of simply supported sandwich plates are developed and used to investigate the limitations and applicability of ESL and LW plate theories for various face-to-core stiffness ratios. In addition to natural frequency results obtained from ESL and LW theories, the solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial finite element method (FEM) software, ABAQUS, are provided. It is found that LW and ESL (even though its higher-order) theories can produce accurate natural frequency results compared to FEM with a considerably lesser number of degrees of freedom. / Doctor of Philosophy / In everyday life, plate-like structures find applications such as boards displaying advertisements, signs on shops and panels on automobiles. These structures are typically nailed, welded, or glued to supports at one or more edges. When subjected to disturbances such as wind gusts, plate-like structures vibrate. The frequency (number of cycles per second) of a structure in the absence of an applied external load is called its natural frequency that depends upon plate's geometric dimensions, its material and how it is supported at the edges. If the frequency of an applied disturbance matches one of the natural frequencies of the plate, then it will vibrate violently. To avoid such situations in structural designs, it is important to know the natural frequencies of a plate under different support conditions. One would also expect the plate to be able to support the designed structural load without breaking; hence knowledge of plate's deformations and stresses developed in it is equally important. These require mathematical models that adequately characterize their static and dynamic behavior. Most mathematical models are based on plate theories. Although plates are three-dimensional (3D) objects, their thickness is small as compared to the in-plane dimensions. Thus, they are analyzed as 2D objects using assumptions on the displacement fields and using quantities averaged over the plate thickness. These provide many plate theories, each with its own computational efficiency and fidelity (the degree to which it reproduces behavior of the 3-D object). Hence, a plate theory can be developed to provide accurately a quantity of interest. Some issues are more challenging for low-fidelity plate theories than others. For example, the greater the plate thickness, the higher the fidelity of plate theories required for obtaining accurate natural frequencies and deformations. Another challenging issue arises when a sandwich structure consists of strong face-sheets (e.g., made of carbon fiber-reinforced epoxy composite) and a soft core (e.g., made of foam) embedded between them. Sandwich structures exhibit more complex behavior than monolithic plates. Thus, many widely used plate theories may not provide accurate results for them. Here, we have used different plate theories to solve problems including those for sandwich structures. The governing equations of the plate theories are solved numerically (i.e., they are approximately satisfied) using the Ritz method named after Walter Ritz and weighted Jacobi polynomials. It is shown that these provide accurate solutions and the corresponding numerical algorithms are computationally more economical than the commonly used finite element method. To evaluate the accuracy of a plate theory, we have analytically solved (i.e., the governing equations are satisfied at every point in the problem domain) equations of the 3D theory of linear elasticity. The results presented in this research should help structural designers.

In this thesis, the effect of semi-geodesic winding on the free vibration characteristics of filament wound composite shells of revolution with variable radii of curvature is studied. The analysis is performed by a semi-analytical solution method which is based on the numerical integration of the finite exponential Fourier transform of the fundamental shell of revolution equations. The governing equations for the free vibration analysis are initially obtained in terms of fundamental shell variables, and they are reduced to a system of first order ordinary differential equations by the application of finite exponential Fourier Transform, resulting in a two point boundary value problem. The boundary value problem is then reduced to a series of initial value problems, and the multisegment numerical integration technique is used in combination with the frequency trial method in order to extract the natural frequencies and determine the mode shapes within a given range of natural frequencies. Previous studies on geodesic winding is extended such that the effect of semi-geodesic winding which rely on the preset friction between the fiber and the mandrel surface on the stiffness and vibration characteristics of filament wound shells of revolution is investigated. Additionally, finite element analysis is employed to compare the results obtained from semi-analytical model solved by numerical integration and finite element model solved by finite element method. Sample results are obtained for filament wound truncated conical and spherical shells of revolution and the effect of the winding pattern on the vibration characteristics of shells of revolution is investigated thoroughly.

O objetivo deste trabalho é verificar a aplicação do Dynamic Design Analysis Method DDAM na análise de estruturas submetidas a carregamentos de choque. Esse método foi desenvolvido pela Marinha Norte Americana e se propõe a estimar esforços inercias provenientes das respostas de equipamentos de bordo, sejam de navios ou submarinos, a cargas impulsivas, mais precisamente, ondas de choque submarinas. Para a compreensão plena dessa metodologia, foi necessário um estudo sobre vibrações e espectros de resposta, tópicos teóricos que fundamentam esse procedimento. Devido à escassez de informações divulgadas por se tratar de conteúdo militar, foi realizado um estudo de caso para uma estrutura simples, uma viga engastada e seus resultados foram comparados com um prévio trabalho publicado. Com isso, foi possível a aplicação do DDAM em uma estrutura mais complexa como o vaso do reator nuclear do tipo PWR de um submarino, ainda que em um modelo simplificado desse equipamento. No entanto, os resultados mostraram a validade do uso do DDAM na análise estrutural dinâmica de equipamentos de uma maneira qualitativa. / The main purpose of this dissertation is to verify the use of the Dynamic Design Analysis Method DDAM in the study of structures subjected to shock loadings. This method was developed by the U.S. Navy and is intended to estimate inertial forces resultant from the response of shipboard equipment, from surface ships or submarines, due to impulsive loads or, more precisely, underwater pressure shock waves. To fully comprehend this method, it was necessary to acknowledge fundamentals of dynamics of structures like free vibrations, response spectrum analysis correlated topics. And due to lack of public information since it is a military technology, a case study of a cantilever beam was done with its results compared to a previous published paper. Then, the DDAM was applied to a more complex structure a PWR nuclear reactor vase simplified model, in order to show the effectiveness of the method in dynamic structural analysis.

In this Thesis, the problem of the Free Vibrations Analysis of Doubly Stiffened Composite, Orthotropic and/or Isotropic, Base Plates or Panels (with Orthotropic Stiffening Plate Strips) is investigated. The composite plate or panel system is made of an Orthotropic and/or Isotropic Base Plate stiffened or reinforced by adhesively bonded Upper and Lower Orthotropic Stiffening Plate Strips. The plates are assumed to be the Mindlin Plates connected by relatively very thin adhesive layers. The general problem under study is considered in terms of three problems, namely Main PROBLEM I Main PROBLEM II and Main PROBLEM III. The theoretical formulation of the Main PROBLEMS is based on a First Order Shear Deformation Plate Theory (FSDPT) that is, in this case, the Mindlin Plate Theory. The entire composite system is assumed to have simple supports along the two opposite edges so that the Classical Levy&#039 / s Solutions can be applied in that direction. Thus, the transverse shear deformations and the rotary moments of inertia of plates are included in the formulation. The very thin, yet elastic deformable adhesive layers are considered as continua with transverse normal and shear stresses. The damping effects in the plates and the adhesive layers are neglected. The sets of the systems of equations of the Mindlin Plate Theory are reduced to a set of the Governing System of First Order Ordinary Differential Equations in the state vector form. The sets of the Governing System for each Main PROBLEM constitute a Two-Point Boundary Value Problem in the y-direction which is taken along the length of the plates. Then, the system is solved by the Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials)which is a relatively semi-analytical and numerical technique. The numerical results and important parametric studies of the natural modes and the corresponding frequencies of the composite system are presented.

In this thesis, the free vibration analysis of anisotropic laminated composite shells of revolution (ALCSOR) is studied. The governing equations are kinematic, constitutive, and motion equations. Geometrically linear strain-displacement equations of Reissner-Naghdi shell theory in combination with first-order shear deformation theory in which transverse shear and rotatory inertia effects are taken into consideration. The constitutive relations are for macrosopically ALCSOR in which statically equivalent force and moment resultants, instead of internal stresses for a single layer, are introduced. Equations of motion for the free vibration problem are obtained by the Hamilton&amp / #8217 / s principle. The derived governing equations for the free vibration analysis of ALCSOR are initially formulated into a system of partial differential equations in terms of fundamental variables. Then, those partial differential equations are reduced to a system of first order ordinary differential equations by applying finite exponential Fourier Transform method resulting in a two point boundary value problem. It has been demonstrated that the application of the finite exponential Fourier transform made it possible to solve the governing equations, comprising the full anisotropic form of the constitutive equations, which was otherwise impossible to solve with the classical Fourier decomposition method. First, the boundary value problem formulated is reduced to a series of initial value problems, then the multisegment numerical integration is used in combination with the frequency trial method in order to find the critical modes within a given range of natural frequencies. A computer code DALSOR is written for the solution of the natural frequencies and mode shapes of mascroscopically ALCSOR. DALSOR is applicable to any general boundary condition at both ends of the shell, and allows for variation of all elastic and geometric properties in the meridional direction. Numerical results are presented, and mainly discussions on the method of solution and the effect of macroscopic anisotropy on modal characteristics, mainly natural frequencies, are made. Various case studies are performed primarily on cylindrical shells in order to investigate the effects of mainly fiber orientation angle, stacking sequence, arbitrary boundary conditions at the edges of the shell, thickness-to-radius ratio on the modal characteristics, mainly natural frequencies. Application of the method of solution has also been demonstrated for a truncated composite spherical shell.

O objetivo deste trabalho é verificar a aplicação do Dynamic Design Analysis Method DDAM na análise de estruturas submetidas a carregamentos de choque. Esse método foi desenvolvido pela Marinha Norte Americana e se propõe a estimar esforços inercias provenientes das respostas de equipamentos de bordo, sejam de navios ou submarinos, a cargas impulsivas, mais precisamente, ondas de choque submarinas. Para a compreensão plena dessa metodologia, foi necessário um estudo sobre vibrações e espectros de resposta, tópicos teóricos que fundamentam esse procedimento. Devido à escassez de informações divulgadas por se tratar de conteúdo militar, foi realizado um estudo de caso para uma estrutura simples, uma viga engastada e seus resultados foram comparados com um prévio trabalho publicado. Com isso, foi possível a aplicação do DDAM em uma estrutura mais complexa como o vaso do reator nuclear do tipo PWR de um submarino, ainda que em um modelo simplificado desse equipamento. No entanto, os resultados mostraram a validade do uso do DDAM na análise estrutural dinâmica de equipamentos de uma maneira qualitativa. / The main purpose of this dissertation is to verify the use of the Dynamic Design Analysis Method DDAM in the study of structures subjected to shock loadings. This method was developed by the U.S. Navy and is intended to estimate inertial forces resultant from the response of shipboard equipment, from surface ships or submarines, due to impulsive loads or, more precisely, underwater pressure shock waves. To fully comprehend this method, it was necessary to acknowledge fundamentals of dynamics of structures like free vibrations, response spectrum analysis correlated topics. And due to lack of public information since it is a military technology, a case study of a cantilever beam was done with its results compared to a previous published paper. Then, the DDAM was applied to a more complex structure a PWR nuclear reactor vase simplified model, in order to show the effectiveness of the method in dynamic structural analysis.

In this study, the &ldquo / Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo / are investigated in detail. Two different Groups of &ldquo / Stiffened Plates&rdquo / will be considered. In the first group, the &ldquo / Type 4&rdquo / and the &ldquo / Type 6&rdquo / of &ldquo / Group I&rdquo / of the &ldquo / Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo / are theoretically analyzed and numerically solved by making use of the &ldquo / Mindlin Plate Theory&rdquo / . Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo / Dynamic System&rdquo / . Some important parametric studies are also presented for each case. In the second group, the &ldquo / Class 2&rdquo / and the &ldquo / Class 3&rdquo / of the &ldquo / Bonded and Stiffened Plate or Panel Systems&rdquo / are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo / Plate Assembly&rdquo / is constructed by bonding &ldquo / Stiffening Plate Strips&rdquo / to a &ldquo / Base Plate or Panel&rdquo / by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo / Base Plate or Panel&rdquo / by these &ldquo / Stiffening Strips&rdquo / in the appropriate locations, so that the &ldquo / Base Plate or Panel&rdquo / will exhibit satisfactory dynamic response. The forementioned &ldquo / Bonded and Stiffened Systems&rdquo / may also be used to repair a damaged (or rather cracked) &ldquo / Base Plate or Panel&rdquo / . Here in the analysis, the &ldquo / Base Plate or Panel&rdquo / , the &ldquo / Stiffening Plate Strips&rdquo / as well as the in- between &ldquo / adhesive layers&rdquo / are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo / Orthotropic Mindlin Plates&rdquo / . Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo / Group I&rdquo / and &ldquo / Group II&rdquo / problems, the &ldquo / Governing System of Dynamic Equations&rdquo / for every problem is reduced to the &ldquo / First Order Ordinary Differential Equations&rdquo / . In other words the &ldquo / Free Vibrations Problem&rdquo / , in both cases, is an &ldquo / Initial and Boundary Value Problem&rdquo / is reduced to a &ldquo / Two- Point or Multi-Point Boundary Value Problem&rdquo / by using the present &ldquo / Solution Technique&rdquo / . For this purpose, these &ldquo / Governing Equations&rdquo / are expressed in &ldquo / compact forms&rdquo / or &ldquo / state vector&rdquo / forms. These equations are numerically integrated by the so-called &ldquo / Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo / . In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo / Boundary Conditions&rdquo / for each structural &ldquo / System&rdquo / . The effects of several important parameters on the natural frequencies of the aforementioned &ldquo / Systems&rdquo / are also investigated and are graphically presented for each &ldquo / Stiffened and Stiffened and Bonded Plate or Panel System&rdquo / . Additionally, in the case of the &ldquo / Bonded and Stiffened System&rdquo / , the significant effects of the &ldquo / adhesive material properties&rdquo / (i.e. the &ldquo / Hard&rdquo / adhesive and the &ldquo / Soft&rdquo / adhesive cases) on the dynamic response of the &ldquo / plate assembly&rdquo / are also presented.