O ensaio de simples reconhecimento de solos (SPT) é a ferramenta de investigação de solos mais utilizada no mundo. Devido ao grande número de parâmetros que influenciam os seus resultados, a medida de sua eficiência passa a ser indispensável à transposição de experiências entre as práticas desenvolvidas em diferentes locais. Infelizmente, a medida da eficiência através da instrumentação do impacto do martelo é economicamente inviável para a maioria das empresas de sondagem no Brasil. Este trabalho apresenta uma metodologia para a determinação da eficiência do SPT baseada no princípio de Hamilton e na realização de prova de carga estática sobre o amostrador, que pode ser uma alternativa para sanar esta situação. / The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.

<p><b>En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet</b></p><p>Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB).</p><p>Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också.</p><p>Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden.</p> / <p>The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique.</p><p>Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed.</p><p>Tests on spruce wood specimens were carried out at a high strain rate (about 10³ s^-1) using the adapted SHPB technique, and for comparison at low (8×10^-3 s^-1) and medium (17 s^-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.</p>

<b>En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet</b> Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB). Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också. Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden. / The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique. Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed. Tests on spruce wood specimens were carried out at a high strain rate (about 103 s-1) using the adapted SHPB technique, and for comparison at low (8×10-3 s-1) and medium (17 s-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.

Courses in analytical mechanics for undergraduate students are often limited to treatment of holonomic constraints, which are constraints on coordinates. The concept of nonholonomic constraints, constraints on velocities, is usually only mentioned briefly and it is easy to get a wrongful idea of what they are and how to treat them. This text explains and compares the methods of deriving the Euler-Lagrange equations and the consequences when imposing different kinds of constraints. One way to properly treat both holonomic and nonholonomic constraints is given, pinpointing the difficulties and common errors. Along the way, the treatment in local coordinates is also put in more modern terms, in the language of differential geometry, which is the language most commonly used in modern texts on the subject.

O ensaio de simples reconhecimento de solos (SPT) é a ferramenta de investigação de solos mais utilizada no mundo. Devido ao grande número de parâmetros que influenciam os seus resultados, a medida de sua eficiência passa a ser indispensável à transposição de experiências entre as práticas desenvolvidas em diferentes locais. Infelizmente, a medida da eficiência através da instrumentação do impacto do martelo é economicamente inviável para a maioria das empresas de sondagem no Brasil. Este trabalho apresenta uma metodologia para a determinação da eficiência do SPT baseada no princípio de Hamilton e na realização de prova de carga estática sobre o amostrador, que pode ser uma alternativa para sanar esta situação. / The standard penetration test (SPT) is the most used soil investigation tool in the world. Due to the great number of variables that influences its results, the measurement of the efficiency becomes imperative to the transposition of experiences between developed practices in different places. Unfortunately, the measurement of the efficiency through the instrumentation of the hammer impact is economically inpracticable to most of the soil investigation firms in Brazil. This work presents a methodology to determinate the SPT efficiency based on the Hamilton\'s principle and on the execution of static load test over the sampler, what seems to be a good alternative to end this situation.

O ensaio de simples reconhecimento com o SPT é um dos mais utilizados para investigação do subsolo nos EUA e no Brasil. Os dados obtidos com este ensaio dinâmico, tais como o índice de resistência à penetração NSPT, classificação do solo e nível freático são usados por diferentes métodos para estimativa de capacidade de carga de fundações rasas e profundas. Para um mesmo solo, o índice NSPT pode ser diferente se diferentes equipamentos forem usados devido ao fato de que diferentes equipamentos de SPT mostram diferentes níveis de eficiência. Em vista disso, uma alternativa para estimar a eficiência do ensaio SPT é utilizando-se o ensaio de prova de carga estática sobre o amostrador. Este ensaio foi implementado para poder avaliar a eficiência do ensaio SPT. Para este fim, foram executados 13 ensaios dinâmicos e 13 ensaios estáticos no campus experimental do Laboratório de Engenharia Civil da UNESP (Bauru). Para estimar a eficiência do ensaio SPT através do ensaio dinâmico, um sistema de aquisição analógico-digital foi utilizado para obter registros de aceleração e força na seção localizada junto ao amostrador SPT. O ensaio dinâmico foi modificado para utilizar várias energias potenciais nominais do martelo e sistemas de elevação. A determinação da eficiência do ensaio através da execução da prova de carga estática foi obtida com base no princípio de Hamilton. Adicionalmente, realizando-se a comparação entre o comportamento de carregamento dinâmico e estático, pode-se obter a resistência estática do sistema amostrador-solo. Esta resistência é calculada utilizando a base de dados obtidas no campo e a aplicação de vários métodos de estimativa como: Aoki et al.(2007), De Souza (2009) e Odebrecht (2003). Os resultados da estimativa da eficiência através do ensaio de prova de carga estática sobre o amostrador mostraram-se consistentes em relação aos valores obtidos com o ensaio dinâmico. Concluiu-se que a execução do ensaio de prova de carga estática sobre, o amostrador é uma alternativa simples e econômica para obter a eficiência do SPT. / The Standard Penetration Test, SPT, is one of the most used one for subsoil information in the USA and Brazil. The data obtained in this dynamic test, such as the penetration resistance index, NSPT, the soil classification and phreatic level are used by different methods to estimate the shallow and deep foundations load capacity. For the same soil, the index NSPT can be different if different equipments are used, because different SPT equipments show different efficiency levels. Having this in mind, an alternative to estimate the essay efficiency of the SPT test is using the static load test (SLT) to the sampler. This test was implemented in order to evaluate the efficiency of SPT. To do so, 13 dynamic tests and 13 static tests were performed in the experimental campus of the State University of São Paulo at Bauru (Unesp- Bauru-Brazil). To estimate the efficiency of the SPT test through the dynamic test, a data acquisition system was used to register accelerations and forces at the located section close to the sampler SPT. The dynamic test was modified so that it would be possible to use many nominal potential energy of the hammer and elevation systems. The estimation of the efficiency made through the SLT tests was based on Hamilton\'s principle. Furthermore, by comparing the dynamic and static behavior, we can get the soil-sampler interface static resistance. This resistance is calculated by using the field data through various estimation methods such as Aoki\'s (2007), De Souza\'s (2009) and Odebrecht\'s (2003). The estimates of the efficiency obtained through SLT test were found to be consistent with those obtained through the SPT modified tests. We conclude that SLT is a simple and non-expensive alternative to obtain the efficiency of SPT equipment.

O ensaio de simples reconhecimento com o SPT é um dos mais utilizados para investigação do subsolo nos EUA e no Brasil. Os dados obtidos com este ensaio dinâmico, tais como o índice de resistência à penetração NSPT, classificação do solo e nível freático são usados por diferentes métodos para estimativa de capacidade de carga de fundações rasas e profundas. Para um mesmo solo, o índice NSPT pode ser diferente se diferentes equipamentos forem usados devido ao fato de que diferentes equipamentos de SPT mostram diferentes níveis de eficiência. Em vista disso, uma alternativa para estimar a eficiência do ensaio SPT é utilizando-se o ensaio de prova de carga estática sobre o amostrador. Este ensaio foi implementado para poder avaliar a eficiência do ensaio SPT. Para este fim, foram executados 13 ensaios dinâmicos e 13 ensaios estáticos no campus experimental do Laboratório de Engenharia Civil da UNESP (Bauru). Para estimar a eficiência do ensaio SPT através do ensaio dinâmico, um sistema de aquisição analógico-digital foi utilizado para obter registros de aceleração e força na seção localizada junto ao amostrador SPT. O ensaio dinâmico foi modificado para utilizar várias energias potenciais nominais do martelo e sistemas de elevação. A determinação da eficiência do ensaio através da execução da prova de carga estática foi obtida com base no princípio de Hamilton. Adicionalmente, realizando-se a comparação entre o comportamento de carregamento dinâmico e estático, pode-se obter a resistência estática do sistema amostrador-solo. Esta resistência é calculada utilizando a base de dados obtidas no campo e a aplicação de vários métodos de estimativa como: Aoki et al.(2007), De Souza (2009) e Odebrecht (2003). Os resultados da estimativa da eficiência através do ensaio de prova de carga estática sobre o amostrador mostraram-se consistentes em relação aos valores obtidos com o ensaio dinâmico. Concluiu-se que a execução do ensaio de prova de carga estática sobre, o amostrador é uma alternativa simples e econômica para obter a eficiência do SPT. / The Standard Penetration Test, SPT, is one of the most used one for subsoil information in the USA and Brazil. The data obtained in this dynamic test, such as the penetration resistance index, NSPT, the soil classification and phreatic level are used by different methods to estimate the shallow and deep foundations load capacity. For the same soil, the index NSPT can be different if different equipments are used, because different SPT equipments show different efficiency levels. Having this in mind, an alternative to estimate the essay efficiency of the SPT test is using the static load test (SLT) to the sampler. This test was implemented in order to evaluate the efficiency of SPT. To do so, 13 dynamic tests and 13 static tests were performed in the experimental campus of the State University of São Paulo at Bauru (Unesp- Bauru-Brazil). To estimate the efficiency of the SPT test through the dynamic test, a data acquisition system was used to register accelerations and forces at the located section close to the sampler SPT. The dynamic test was modified so that it would be possible to use many nominal potential energy of the hammer and elevation systems. The estimation of the efficiency made through the SLT tests was based on Hamilton\'s principle. Furthermore, by comparing the dynamic and static behavior, we can get the soil-sampler interface static resistance. This resistance is calculated by using the field data through various estimation methods such as Aoki\'s (2007), De Souza\'s (2009) and Odebrecht\'s (2003). The estimates of the efficiency obtained through SLT test were found to be consistent with those obtained through the SPT modified tests. We conclude that SLT is a simple and non-expensive alternative to obtain the efficiency of SPT equipment.

Se presenta un modelo de elementos finitos que describe el comportamiento de vibración de libre de vigas compuestas laminadas. Se desarrolla el modelo utilizando el principio de Hamilton y la teoría de vigas Timoshenko que incluye deformaciones por corte. Se asume interpolaciones de alto orden para la aproximación de las variables fundamentales. Los laminados compuestos son ortotrópicos con fibras orientadas en diferentes direcciones. Se implementa un programa para materiales compuestos laminado en MATLAB. Se comparan resultados con otros obtenidos en la literatura para validar el modelo. Se realiza un estudio de convergencia y paramétrico con un mismo número de lámina y diferentes direcciones. Se verifica que la formulación que es bastante precisa con resultados satisfactorios en la investigación. / In this work, is presented a finite element model that describes the free vibration behavior of laminated composite beams. The model is developed by the Hamilton principle and the Timoshenko theory that includes shear deformations. Composite laminates are assumed to be orthotropic with fibers oriented in different directions, such as Angle Ply and Cross Ply cases. This investigation works out on a MAPLE program for laminated composites materials that will be completed all in MATLAB program. In order to validate the model, the results are compared with different literatures, also verify the formulation that is quite accurate and obtain quite satisfactory results in the investigation. High order interpolations are assumed to approximate fundamental variables. A convergence study and parametric study will be carried out with the same number of laminas in different directions. / Tesis

El presente trabajo, tiene como objetivo el estudio de la vibración libre de vigas Timoshenko aplicados a materiales funcionalmente graduados; esto se resuelve utilizando el método de elementos finitos (MEF) , al implementarlo en el software MATLAB, con el fin de obtener las frecuencias fundamentales y las gráficas de los modos de vibración para cada caso. Se define el campo de desplazamientos según la teoría Timoshenko considerando tres variables fundamentales; asimismo, se utiliza el Principio de Hamilton para obtener las vibraciones libres del elemento. Para el desarrollo de las relaciones constitutivas se usa la La ley de potencia, el cual describe como varían las propiedades de un material heterogéneo e isotrópico FGM (FGM por sus siglas en inglés) en el peralte de la viga. Los resultados obtenidos se compararon con otros estudios de la literatura validados por revistas como SCOPUS y SPRINGER, demostrando que el modelo es bastante preciso y satisfactorio. / The present work aims to study the free vibration of Timoshenko beams applied to functionally graduated materials; This is solved using the finite element method (FEM), when implemented in the MATLAB software, in order to obtain the fundamental frequencies and the graphs of the vibration modes for each case. The field of displacements is defined according to the Timoshenko theory considering three fundamental variables; likewise, the Hamilton Principle is used to obtain the free vibrations of the element. For the development of the constitutive relationships, the power law is used, which describes how the properties of a heterogeneous and isotropic material FGM vary in the heightn of the beam. The results obtained were compared with other literature studies validated by journals such as SCOPUS and SPRINGER, showing that the model is quite accurate and satisfactory. / Tesis

The lowest natural frequencies of thin-walled noncircular fiber-reinforced composite cylinders, specifically cylinders with elliptical cross sections, are investigated. Of interest is the variation of the lowest natural frequency, the so-called fundamental frequency, as a function of wall laminate properties, cross-sectional eccentricity and other cylinder geometric parameters. Both simple and clamped support boundary conditions are investigated. Laminate properties that are uniform with circumferential location and laminate properties that vary with circumferential location, by way of varying laminate fiber angle with circumferential location, are considered. As the radius of curvature of a noncircular cylinder varies with circumferential location, it is logical to consider the influence of circumferentially varying fiber orientation on the fundamental frequency. The analysis for predicting the fundamental frequency is based on Donnell shell theory, linear elastic properties, and the use of Hamilton's Principle in conjunction with the Rayleigh-Ritz technique. By use of a so-called shape factor, the magnitude of cylinder normal displacements are modulated to be larger in the regions of the cross section with the largest radius of curvatures and smaller in the regions with the smallest radius of curvature. The final equations for predicting the fundamental frequency are quite complex, but a series of approximations results in a hierarchy of simpler equations, the simplest being referred to as Lo's approximation. The prediction of the fundamental frequencies is spot checked by comparing the results as predicted by the various levels of approximation with predictions of a shell-based finite element model. Considering uniform laminate properties, comparisons between the developed analysis and the finite element model are good for all levels of simpler equations, and excellent in some cases. The developed analysis is subsequently used for parameter studies. It is found that compared to a circular cylinder of the same circumference and with uniform laminate properties, the fundamental frequency of an elliptical cylinder is always less. Surprisingly, based on the results obtained, it appears that for a given cylinder geometry the fundamental frequency is not particularly sensitive to wall lamination sequence, though the wave number in the circumferential direction of the mode shape associated with the fundamental frequency is sensitive to lamination sequence. Considering cylinders with circumferentially varying fiber orientation, comparisons between the developed analysis and the finite element model for most of the cases studied are good. However, the developed equations are limited since it is difficult to find a set of known functions to describe the deformation of an arbitrary lamination sequence when applying the Rayleigh-Ritz technique. In general, in can be concluded that the effect of varying fiber orientation on the fundamental frequency is much less than the influence of cylinder aspect ratio. It can also be concluded that the developed analysis would be an excellent tool for design purposes, as the calculation of the fundamental frequency is done quickly, and design trade-offs studies would be easy. / Ph. D.