This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.

This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.

The random wetlay process is used to make fiber-reinforced thermoplastic sheets that can be compression molded into composite panels at little cost. By utilizing these composite panels as the facesheets of honeycomb sandwich structures, it is possible to greatly increase the bending stiffness of the composite without adding significant weight. The random wetlay composite facesheets used in this research consisted of 25% E-glass fibers and 75% PET by weight. The thickness uniformity of the facesheets was difficult to control. The core of the sandwich structure was HexWeb&174; EM. Three low-cost adhesives were examined for secondarily bonding the facesheets to the core: polyurethane glue; epoxy paste; and 3M Scotch-Grip&174; plastic adhesive. The polyurethane glue mixed with Cab-O-Sil filler was easiest to apply and provided the largest flatwise tensile strength. Mathematical models were developed to predict the static behavior of sandwich beams and plates in bending. Three-point bend tests were performed on a sandwich beam in accordance with ASTM C 393. A sandwich plate simply supported along two opposite edges and free along the other two edges was subjected to a line-load using weights and a wiffle tree arrangement. An effective facesheet modulus and Poisson's ratio were found by comparing the measured displacements to the sandwich plate theory. The shadow moiré technique was used to visualize the displacement of the line-loaded sandwich plate. The overall shape of the displacement was very similar to the shape predicted by the sandwich plate theory. / Master of Science

Accurately modeling damping in engineering structures has plagued scientist and engineers for decades. The integration of viscoelastic materials into engineering structures can reduce undesired vibrations and serve as an effective passive control mechanism. Various techniques have been developed to model viscoelastic materials. The growing popularity of finite element analysis in the 1980s and 1990s spawned new techniques for modeling damping in complex structures. The technique defined in this dissertation can be incorporated into finite element models. In metals, the modulus of elasticity can be modeled as a constant. That is, the modulus of elasticity is not treated as a function of frequency in dynamic models. For viscoelastic materials, the modulus of elasticity can be assumed to be constant for static forces and sinusoidal forcing functions. However, when viscoelastic materials undergo excitations from a random or transient forcing function the constant modulus of elasticity assumption may not be valid. This is because the second order equation of motion has non-constant coefficients or coefficients that vary as a function of frequency. The Golla-Hughes-McTavish (GHM) method is a technique used to incorporate the frequency dependency of viscoelastic materials into finite element models. The GHM method is used as a way to alleviate working with second order differential equations with non-constant coefficients. This dissertation presents the theory for a new material modulus function suitable for application within the framework of the GHM method. However, the new material modulus function uses different assumptions and is referred to as the Modified GHM method or MGHM method. The MGHM method is shown to improve the curve fit and damping characteristics of the GHM method. Additionally, the MGHM method is shown to reduce to the GHM method when the original GHM assumptions are imposed. / Ph. D.

In an effort to achieve lighter and more economical space structures, a new patented steel composite member has been suggested and used in the construction of some steel roof structures. This special element has a sandwich construction composed of some strips of steel plates placed longitudinally along a helical wire core. The function of the helical core is to transfer the shear between the flange plates and increase the sectional inertia of the resulting composite member by keeping the flange plates at a desired distance from each other. Because of the lack of research, design engineers usually treat such elements as a solid member as if it has a full shear transfer between the flanges. However, a detailed analysis shows that this is not a valid assumption and leads to very unsafe results. In this context, the purpose of this study is to investigate the behavior of such members under axial compression and determine their effective sectional flexural rigidity by taking into account the shear deformations. This study applies an analytical investigation to a specific form of such elements with four flange plates placed symmetrically around a helical wire core. Five independent parameters of such a member are selected for this purpose. These are the spiral core and core wire diameters, the pitch of the spiral core, and the flange plate dimensions. Elements with varying combinations of the selected parameters are first analyzed in detail by finite element method, and some design charts are generated for the determination of the effective sectional properties to be used in the structural analysis and the buckling loads. For this purpose, an alternative closed-form approximate analytical solution is also suggested.

Resumo: Neste trabalho é apresentado uma proposta de absorvedor de vibrações ajustável tipo viga sanduíche utilizando fluido Magnetoreológico no centro. Para o desenvolvimento deste projeto foi realizada uma revisão sobre os vários tipos de absorvedores e algumas aplicações. Em seguida foi realizado um estudo sobre o comportamento do fluido magnetoreológico, mostrando como este material inteligente varia suas propriedades quando submetido a um campo magnético. O objetivo do estudo foi verificar as propriedades do sistema para realização de um futuro controle, que é realizado através da variação do campo magnético. Avaliou-se, também, a relação com a corrente elétrica, quais os parâmetros que o influenciam e como podemos produzir um campo magnético com a intensidade desejada. Para avaliar as características do sistema foi utilizado o modelo no programa Ansys, com o objetivo de se verificar o comportamento do sistema. Para encontrar as características reais do sistema foi utilizado o modelo na forma de espaço de estados modais, identificado através do método PEM, Método de Predição de Erros (do inglês Prediction Error Methods ���� PEM). Os testes experimentais foram realizados para se adquirir conhecimento do comportamento dinâmico deste tipo de fluido e, verificar se há repetibilidade nas medidas / Abstract: This work presents a proposal of a tunable vibrations absorber type sandwich beam, using the Magnetorheologic fluid in the intermediate layer. For the development of this study a revision of some types of absorber with some applications was carried out. After that, a study of the behavior of the magnetorheologic fluid was carried through, showing as this intelligent material tunable its properties when submitted to a magnetic field. The objective of this analysis was to verify the properties of the system for implementation of a future control, which is based on the variation of the magnetic field. It was realized an analysis of the relation of the electric current and the parameters that influence it, in order to produce a magnetic field with the desired intensity. The characteristics of the system were verified through a mathematical model obtained with the software Ansys. The real characteristics of the system were found through the identification method PEM, Prediction Error Methods, using modal space states formulation. Experimental tests were carried out in order to obtain know how of the dynamic behavior of this type of material / Orientador: Vicente Lopes Junior / Coorientador: Michael J. Brennan / Banca: Hermes Adolfo de Aquino / Banca: Edson Antonio Capello Sousa / Mestre

Textile Reinforced Concrete (TRC) with a small thickness, high tensile and compressive strength has been combined with lightweight materials to create sandwich elements. Due to the low strength of the core materials in the sandwich elements, the additional shear connector devices were suggested to improve the load capacity. However, it raised an idea of using a higher strength material core, Expanded Polystyrene Concrete (EPC), without any connector devices to create a new type of lightweight sandwich element, which can be an answer for not only developing lightweight structures but also solving environmental problems. In this thesis, this novel idea was gradually realized with a study on TRC-EPC sandwich beams. Firstly, experimental material tests on EPC showed the possibility to recycle EPS waste for EPC with a density of around 950 kg/m3. Thus, an EPC with a density of 920 kg/m3 and a compressive strength of 5.2 N/mm2 was chosen for the core to realize the concept for TRC-EPC sandwich with 18 experimental beams. Bending tests of six series with shear-to-depth-ratio (a/d) from 1.5 to 5.2 were implemented to study load responses of this type of sandwich beam. The failure moments of all the specimens were smaller than the nominal moment strength of the cross section. The load capacities of the specimens depend strongly on the ratio a/d. The calculations for the shear capacity according to standards as well as shear calculation approaches were implemented. Due to their generalized form, ACI 318-05 and EC2 offer conservative results for a/d<5.2. The dependence of the shear capacity on a/d could be better described with CEB-FIB Model Code 1990. For the beams with 1.5<a/d and a/d<2.1, Strut and Tie Model gave the most suitable results. In case a/d>2.1, ZINK’s model offered better results than the others. Besides, a new proposed equation for the shear capacity of TRC-EPC sandwich beams depending on the a/d was also suggested. In order to model the load response of the six experimental series, FEM models with ATENA developed. The models with and without a consideration of the bond between the textile and fine HSC in the TRC layer underestimated the load capacity with tolerance 26% and 28 % respectively. The tolerances for the deflections in the models with a/d>2.5 were around 22 % and 23%. Finally, an engineering model originally based on sandwich theory was developed to model the load-deflection response of this type of sandwich beams. The model could predict the displacement with tolerances from -24 % to 12 %. The load capacity of TRC-EPC sandwich beams was underestimated with a tolerance in the range of 15- 34 %. / In dieser Arbeit wurde eine neue Sandwichkonstruktion untersucht, für die Textilbeton, ein Werkstoff mit geringer Dicke und gleichzeitig hoher Zug- und Druckfestigkeit, mit leichten Kernmaterialien kombiniert wurde. Aufgrund der geringen Festigkeit der Kernmaterialien werden in vielen Sandwichkonstruktionen zusätzliche Schubverbinder benötigt, um eine ausreichende Tragfähigkeit zu erreichen. Dies führte zu der Idee, Expanded Polystyrene Concrete (EPC) als höherfestes Kernmaterial zu verwenden, das keine zusätzlichen Verbindungsmittel benötigt. Damit entsteht eine neuartige Sandwichkonstruktion, die nicht nur eine Lösung für die Entwicklung neuer leichter Strukturen ist, sondern auch für Umweltprobleme. Diese Idee wurde in dieser Arbeit durch theoretische und experimentelle Untersuchungen an Textilbeton-EPC-Sandwichbalken umgesetzt. Zunächst wurden Materialuntersuchungen an EPC durchgeführt, um nachzuweisen, dass es möglich ist, EPC mit einer Dichte von rund 950 kg/m³ mit recyceltem EPS herzustellen. Für die anschließenden Untersuchungen an 18 Sandwichbalken wurde dann ein EPC mit einer Dichte von 920 kg/m³ und einer Druckfestigkeit von 5,2 N/mm² ausgewählt. In 6 Serien von Sandwichbalken wurden 4-Punkt-Biegeversuche mit Schubschlankheiten von 1,5 bis 5,2 durchgeführt. Die Bruchmomente aller Balken waren geringer als die rechnerische Momententragfähigkeit des Querschnitts und die Tragfähigkeit war stark von der Schubschlankheit abhängig. Es wurden Berechnungen zur Schubtragfähigkeit nach den verschiedenen internationalen Normen durchgeführt. Aufgrund ihrer allgemeingültigen Form ergaben ACI 318-05 und EC2 sehr konservative Ergebnisse für Schubschlankheiten kleiner als 5,2. Die Formulierung des CEB-FIB Model Code 1990 war besser geeignet, die Abhängigkeit der Schubtragfähigkeit von der Schubschlankheit abzubilden. Für die Balken mit Schubschlankheiten a/d=1,5 bis 2,1 brachten Stabwerkmodelle ausreichend gute Ergebnisse. In Fällen mit a/d>2,1 ergab das Modell von Zink die besten Übereinstimmungen. Um die Abhängigkeit der Schubtragfähigkeit von der Schubschlankheit besser erfassen zu können, wurde eine neue Berechnungsgleichung für Textilbeton-EPC-Balken vorgeschlagen. Um das Last-Verformungsverhalten der experimentellen Untersuchungen beschreiben zu können, wurden FEM-Modelle mit der Software ATENA entwickelt. Es wurden verschiedene Modelle untersucht, die den Verbund zwischen dem textilen Gelege und dem Feinbeton unterschiedlich stark berücksichtigten. Die Tragfähigkeit der untersuchten Balken wurde mit den FEM-Modellen um ca. 26% bis 28% unterschätzt. Die Abweichungen in den berechneten Durchbiegungen betrugen für die Balken mit a/d>2,5 ca. 22% bis 23%. Abschließend wurde ein Ingenieurmodell auf Grundlage der Sandwichtheorie entwickelt, mit dem das Last-Verformungsverhalten dieser Sandwichkonstruktion gut beschrieben werden kann. Mit dem Modell ergaben sich Abweichungen von -24% bis +12% zwischen experimentellen und theoretisch ermittelten Verformungen. Die Tragfähigkeit wurde mit einer Abweichung von 15% bis 34% unterschätzt.

Made available in DSpace on 2014-06-11T19:27:13Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-02-29Bitstream added on 2014-06-13T19:35:06Z : No. of bitstreams: 1 mesquitaneto_c_me_ilha.pdf: 1673109 bytes, checksum: 0f8131abf5fc45715c92abece81e6a7a (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho é apresentado uma proposta de absorvedor de vibrações ajustável tipo viga sanduíche utilizando fluido Magnetoreológico no centro. Para o desenvolvimento deste projeto foi realizada uma revisão sobre os vários tipos de absorvedores e algumas aplicações. Em seguida foi realizado um estudo sobre o comportamento do fluido magnetoreológico, mostrando como este material inteligente varia suas propriedades quando submetido a um campo magnético. O objetivo do estudo foi verificar as propriedades do sistema para realização de um futuro controle, que é realizado através da variação do campo magnético. Avaliou-se, também, a relação com a corrente elétrica, quais os parâmetros que o influenciam e como podemos produzir um campo magnético com a intensidade desejada. Para avaliar as características do sistema foi utilizado o modelo no programa Ansys, com o objetivo de se verificar o comportamento do sistema. Para encontrar as características reais do sistema foi utilizado o modelo na forma de espaço de estados modais, identificado através do método PEM, Método de Predição de Erros (do inglês Prediction Error Methods PEM). Os testes experimentais foram realizados para se adquirir conhecimento do comportamento dinâmico deste tipo de fluido e, verificar se há repetibilidade nas medidas / This work presents a proposal of a tunable vibrations absorber type sandwich beam, using the Magnetorheologic fluid in the intermediate layer. For the development of this study a revision of some types of absorber with some applications was carried out. After that, a study of the behavior of the magnetorheologic fluid was carried through, showing as this intelligent material tunable its properties when submitted to a magnetic field. The objective of this analysis was to verify the properties of the system for implementation of a future control, which is based on the variation of the magnetic field. It was realized an analysis of the relation of the electric current and the parameters that influence it, in order to produce a magnetic field with the desired intensity. The characteristics of the system were verified through a mathematical model obtained with the software Ansys. The real characteristics of the system were found through the identification method PEM, Prediction Error Methods, using modal space states formulation. Experimental tests were carried out in order to obtain know how of the dynamic behavior of this type of material

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-01-16T16:28:17Z No. of bitstreams: 1 waldirnemefelippefilho.pdf: 5861193 bytes, checksum: 8e75fc60830c02857375c1b6cd363132 (MD5) / Approved for entry into archive by Diamantino Mayra (mayra.diamantino@ufjf.edu.br) on 2017-01-31T10:34:29Z (GMT) No. of bitstreams: 1 waldirnemefelippefilho.pdf: 5861193 bytes, checksum: 8e75fc60830c02857375c1b6cd363132 (MD5) / Made available in DSpace on 2017-01-31T10:34:29Z (GMT). No. of bitstreams: 1 waldirnemefelippefilho.pdf: 5861193 bytes, checksum: 8e75fc60830c02857375c1b6cd363132 (MD5) Previous issue date: 2016-08-25 / As estruturas atuais de engenharia civil têm apresentado pronunciado comportamento dinâmico, impondo a necessidade de se veri car, durante a fase de projeto, este comportamento. Apesar dessas veri cações e das recomendações normativas, algumas estruturas apresentam grandes amplitudes de deslocamentos ao experimentarem combinações de ações imprevistas, sendo necessária a aplicação de um sistema para controle de vibrações. Uma forma e ciente de controle destas estruturas é através de sistemas passivos via materiais viscoelásticos (MVE). Modelos determinísticos são numerosos na literatura e conseguem aproximar relativamente bem o comportamento dinâmico de estruturas amortecidas via MVE. Esses modelos, porém, são incapazes de capturar as incertezas associadas, por exemplo, às propriedades mecânicas dos materiais. Uma forma para capturar essas incertezas é através da modelagem não determinística. Neste sentido, este trabalho discutirá a modelagem numérica dos MVE abordando alguns dos fatores que in uenciam o desempenho de modelos numéricos, estratégias para ajuste dos parâmetros que de nem o comportamento dependente da frequência desses materiais e apresentará uma proposta de um modelo não determinístico. Comparam-se as frequências naturais e taxas de amortecimento de vigas sanduíche identi cadas com os resultados obtidos com o modelo proposto e aqueles obtidos através de ensaios experimentais. Pretende-se com este modelo fornecer ao projetista, ao invés de um único valor para os parâmetros modais da estrutura e deslocamentos, uma representação probabilística. / The current civil engineering structures have shown pronounced dynamic behavior, imposing the need to check, during the design phase, this behavior. Despite these veri cations and normative recommendations, some structures experience large amplitudes of displacements under unexpected actions, then a vibration control system is required. An e cient way to control these structures is through passive vibration control systems with viscoelastic materials (VEM). Deterministic models are numerous in literature and they present fairly good approximations for the dynamics behavior of structures damped with VEM. These models however are unable to capture uncertainties associated, for instance, with the mechanical properties of materials. One way to capture these uncertainties is through non-deterministic models. Thus, this thesis discusses the numerical modeling of MVE addressing some of the factors that in uence the performance of numerical models, some strategies to adjust the parameters that de ne the frequency dependent behavior of these materials and present a proposal for a non-deterministic model. The aim of this model is provide to the designer, rather than a single value for the structures modal parameters and displacements, a probabilistic representation.

Textile Reinforced Concrete (TRC) with a small thickness, high tensile and compressive strength has been combined with lightweight materials to create sandwich elements. Due to the low strength of the core materials in the sandwich elements, the additional shear connector devices were suggested to improve the load capacity. However, it raised an idea of using a higher strength material core, Expanded Polystyrene Concrete (EPC), without any connector devices to create a new type of lightweight sandwich element, which can be an answer for not only developing lightweight structures but also solving environmental problems. In this thesis, this novel idea was gradually realized with a study on TRC-EPC sandwich beams. Firstly, experimental material tests on EPC showed the possibility to recycle EPS waste for EPC with a density of around 950 kg/m3. Thus, an EPC with a density of 920 kg/m3 and a compressive strength of 5.2 N/mm2 was chosen for the core to realize the concept for TRC-EPC sandwich with 18 experimental beams. Bending tests of six series with shear-to-depth-ratio (a/d) from 1.5 to 5.2 were implemented to study load responses of this type of sandwich beam. The failure moments of all the specimens were smaller than the nominal moment strength of the cross section. The load capacities of the specimens depend strongly on the ratio a/d. The calculations for the shear capacity according to standards as well as shear calculation approaches were implemented. Due to their generalized form, ACI 318-05 and EC2 offer conservative results for a/d<5.2. The dependence of the shear capacity on a/d could be better described with CEB-FIB Model Code 1990. For the beams with 1.5<a/d and a/d<2.1, Strut and Tie Model gave the most suitable results. In case a/d>2.1, ZINK’s model offered better results than the others. Besides, a new proposed equation for the shear capacity of TRC-EPC sandwich beams depending on the a/d was also suggested. In order to model the load response of the six experimental series, FEM models with ATENA developed. The models with and without a consideration of the bond between the textile and fine HSC in the TRC layer underestimated the load capacity with tolerance 26% and 28 % respectively. The tolerances for the deflections in the models with a/d>2.5 were around 22 % and 23%. Finally, an engineering model originally based on sandwich theory was developed to model the load-deflection response of this type of sandwich beams. The model could predict the displacement with tolerances from -24 % to 12 %. The load capacity of TRC-EPC sandwich beams was underestimated with a tolerance in the range of 15- 34 %. / In dieser Arbeit wurde eine neue Sandwichkonstruktion untersucht, für die Textilbeton, ein Werkstoff mit geringer Dicke und gleichzeitig hoher Zug- und Druckfestigkeit, mit leichten Kernmaterialien kombiniert wurde. Aufgrund der geringen Festigkeit der Kernmaterialien werden in vielen Sandwichkonstruktionen zusätzliche Schubverbinder benötigt, um eine ausreichende Tragfähigkeit zu erreichen. Dies führte zu der Idee, Expanded Polystyrene Concrete (EPC) als höherfestes Kernmaterial zu verwenden, das keine zusätzlichen Verbindungsmittel benötigt. Damit entsteht eine neuartige Sandwichkonstruktion, die nicht nur eine Lösung für die Entwicklung neuer leichter Strukturen ist, sondern auch für Umweltprobleme. Diese Idee wurde in dieser Arbeit durch theoretische und experimentelle Untersuchungen an Textilbeton-EPC-Sandwichbalken umgesetzt. Zunächst wurden Materialuntersuchungen an EPC durchgeführt, um nachzuweisen, dass es möglich ist, EPC mit einer Dichte von rund 950 kg/m³ mit recyceltem EPS herzustellen. Für die anschließenden Untersuchungen an 18 Sandwichbalken wurde dann ein EPC mit einer Dichte von 920 kg/m³ und einer Druckfestigkeit von 5,2 N/mm² ausgewählt. In 6 Serien von Sandwichbalken wurden 4-Punkt-Biegeversuche mit Schubschlankheiten von 1,5 bis 5,2 durchgeführt. Die Bruchmomente aller Balken waren geringer als die rechnerische Momententragfähigkeit des Querschnitts und die Tragfähigkeit war stark von der Schubschlankheit abhängig. Es wurden Berechnungen zur Schubtragfähigkeit nach den verschiedenen internationalen Normen durchgeführt. Aufgrund ihrer allgemeingültigen Form ergaben ACI 318-05 und EC2 sehr konservative Ergebnisse für Schubschlankheiten kleiner als 5,2. Die Formulierung des CEB-FIB Model Code 1990 war besser geeignet, die Abhängigkeit der Schubtragfähigkeit von der Schubschlankheit abzubilden. Für die Balken mit Schubschlankheiten a/d=1,5 bis 2,1 brachten Stabwerkmodelle ausreichend gute Ergebnisse. In Fällen mit a/d>2,1 ergab das Modell von Zink die besten Übereinstimmungen. Um die Abhängigkeit der Schubtragfähigkeit von der Schubschlankheit besser erfassen zu können, wurde eine neue Berechnungsgleichung für Textilbeton-EPC-Balken vorgeschlagen. Um das Last-Verformungsverhalten der experimentellen Untersuchungen beschreiben zu können, wurden FEM-Modelle mit der Software ATENA entwickelt. Es wurden verschiedene Modelle untersucht, die den Verbund zwischen dem textilen Gelege und dem Feinbeton unterschiedlich stark berücksichtigten. Die Tragfähigkeit der untersuchten Balken wurde mit den FEM-Modellen um ca. 26% bis 28% unterschätzt. Die Abweichungen in den berechneten Durchbiegungen betrugen für die Balken mit a/d>2,5 ca. 22% bis 23%. Abschließend wurde ein Ingenieurmodell auf Grundlage der Sandwichtheorie entwickelt, mit dem das Last-Verformungsverhalten dieser Sandwichkonstruktion gut beschrieben werden kann. Mit dem Modell ergaben sich Abweichungen von -24% bis +12% zwischen experimentellen und theoretisch ermittelten Verformungen. Die Tragfähigkeit wurde mit einer Abweichung von 15% bis 34% unterschätzt.