Finite element analysis of laminated shells using a three-noded flat triangular shell element is presented. The flat shell element is obtained by combining the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element similar to the Allman element, but derived from the Linear Strain Triangular (LST) element. Though this combination has been employed in the literature for linear static analysis of laminated plates, the results presented are not adequate to ascertain that the element would perform well in the case of static and dynamic analysis of general shells. The element is first thoroughly tested for linear static analysis of laminated plates and shells and is extended for free vibration, thermal, and geometrically nonlinear analysis. The major drawback of the DKT plate bending element is that the transverse displacement is not explicitly defined within the interior of the element. Hence obtaining the consistent mass matrix or the derivatives of the transverse displacement that are required for forming the geometric stiffness matrix is not straight forward. This problem is alleviated by borrowing shape functions from other similar elements or using simple displacement fields. In the present research, free vibration analysis is performed both by using a lumped mass matrix and a so called consistent mass matrix, obtained by borrowing shape functions from an existing element, in order to compare the performance of the two methods. The geometrically nonlinear analysis is performed using an updated Lagrangian formulation employing Green strain and Second Piola-Kirchhoff (PK2) stress measures. A linear displacement field is used for the transverse displacement in order to compute the derivatives of the transverse displacement that are required to compute the geometric stiffness or the initial stress matrix. Several numerical examples are solved to demonstrate the accuracy of the formulation for both small and large rotation analysis of laminated plates and shells. The results are compared with those available in the existing literature and those obtained using the commercial finite element package ABAQUS and are found to be in good agreement. The element is employed for two main applications involving large flexible structures. The first application is the control of thermal deformations of a spherical mirror segment, which is a segment of a multi-segmented primary mirror used in a space telescope. The feasibility of controlling the surface distortions of the mirror segment due to arbitrary thermal fields, using discrete and distributed actuators, is studied. This kind of study was required for the design of a multi-segmented primary mirror of a next generation space telescope. The second application is the analysis of an inflatable structure, being considered by the US Army for housing vehicles and personnel. The tent structure is made up of membranes supported by arches stiffened by internal pressure. The updated Lagrangian formulation of the flat shell element has been developed primarily for the nonlinear analysis of the tent structure, since such a structure is expected to undergo large deformations and rotations under the action of environmental loads like the wind and snow loads. The wind load is modeled as a nonuniform pressure load and the snow load as lumped concentrated loads. Since the direction of the pressure load is assumed to be normal to the current configuration of the structure, it changes as the structure undergoes deformation. This is called the follower action. As a result, the pressure load is a function of the displacements and hence contributes to the tangent stiffness matrix in the case of geometrically nonlinear analysis. The thermal load also contributes to the system tangent stiffness matrix. In the case of the thermal load this contribution is similar to the initial stress matrix and hence no additional effort is required to compute this contribution. In the case of the pressure load, this contribution (called the pressure stiffness) is in general unsymmetric but can be systematically derived from the principle of virtual work. The follower effects of the pressure load have been included in the updated Lagrangian formulation of the flat shell element and have been validated using standard examples in the literature involving deformation-dependent pressure loads. The element can be used to obtain the nonlinear response of the tent structure under wind and snow loads. / Ph. D.

A self-sensing and self-healing bolted joint has been developed. This concept encompasses the areas of health monitoring, joint dynamics and smart materials. In order to detect looseness in a joint the impedance health monitoring method is used. A new method of making impedance measurements for health monitoring that greatly reduces the equipment cost and equipment size was developed. This facilitates implementation of the impedance technique in real-life field applications. Several proof of concept experiments are presented and compared to the traditional method of making impedance measurements. Investigations of bolted joint dynamics were conducted. A literature review of bolted joints and their diagnostics is presented. The application of the transfer impedance method is compared to standard modal tests on various bolt tensions. An investigation of damping in bolted joints was also made comparing a bolted and monolithic beam. Practical issues in adaptive bolted joints are investigated. This includes issues on activating/heating SMA actuators, connecting the actuators to the power source, size selection of SMA actuators and insulations. These issues are examined both experimentally and theoretically. / Master of Science

Passive control techniques to minimize structural vibrations are limited with respect to the amount of attenuation obtained especially in the low-frequency region but do not require adding any power. Active control methods are effective for reducing structural vibrations, especially at low frequencies, but may require significant control effort. Thus, passive and active control methods have complementary frequency ranges of application. This research consists of combining active and passive control techniques to simultaneously attenuate extensional and flexural power flows in infinite thin beams and determine the advantages and disadvantages of such a combination. An analytical model is developed for an infinite beam with a passive insert of high damping placed at some distance from a point force excitation (passive approach). The passive control of vibrations results in a reduction of both extensional and flexural power flows downstream of the passive material discontinuity. The simultaneous active control of extensional and flexural waves, using two co-located independent piezoceramic actuators bonded to the surface of the beam, is theoretically studied. The active control model shows that the use of two independent piezoceramic actuators allows complete cancellation of the total power flow (sum of the extensional and flexural power flows) downstream of the actuators. The combination of passive and active control methods for three different configurations (actuators located upstream of, downstream of, and on the passive insert) is investigated and complete control of the total power flow is again achieved. The results demonstrate that in the case of the actuators bonded to the passive material discontinuity, the active/passive combination has great potential for reducing the control effort required for the active controller. Finally, an approximation of the influence of heavy fluid flanking paths on the optimal active/passive system is developed by simulation of these flanking paths using axial and torsional springs. This last study shows that both axial and torsional springs will result in modification of the control effort required by the actuators if their respective stiffness is greater than the equivalent stiffness of the section in parallel with the springs. / Master of Science

Of primary importance to the design and application of adaptive structures is a modeling method to allow for performance prediction and parametric optimization of the integrated system. The statics-based modeling approaches have been applied to model piezoelectric (PZT) actuator-driven adaptive structures. The dynamic interaction between the actuators and their host structures has been ignored, and the system energy conversion can’t be predicted. As a matter of fact, PZT actuator-driven smart structures are complex electromechanical coupling systems in which electrical energy is converted into mechanical energy and vice-versa. The actuator outputs and the system energy conversion are dominated by the complex electro-mechanical impedance of the system. The entire actuator/substrate system can thus be essentially represented by a coupled impedance-based system model. This research presents such an impedance-based electro-dynamics analytical method and the experimental investigation for integrated PZT/substrate systems. When compared with the conventional static models, the system modeling method has revealed the physical essence and the interconnections among the intelligent elements and supporting structures. The frequency-dependent behaviors of the actuator and the dynamic response of the integrated system are accurately predicted. The theoretical model was developed for generic PZT actuator-driven active structures. The actuation force was evaluated as a result of the dynamic interaction between the actuator and the host structure. The model was then extended to include the electrical parameters of the PZT actuator such that the power flow and consumption of the integrated system can be predicted. The system dissipative power was then treated as the equivalent generation source to evaluate a temperature rise and thermal damage of the actuator. To examine the utility and generality of the system modeling method, the developed model was applied to typical two-dimensional structures such as thin plates and thin shells, and to one-dimensional structures such as the circular rings and beams. The design-related mechanical and thermal stress characteristics of the actuators were also specifically investigated. In addition to the theoretical work, experiments were conducted. The PZT actuator-driven simply-supported plate was built and tested. The velocity response of the integrated plate and the dynamic strain of the PZT actuators were measured. The coupled electromechanical admittance of the real system was also directly measured using an impedance analyzer. The predicted solutions agree with the experimental results in all of the tested cases, verifying the theoretical model. / Ph. D.

Induced strain actuators have been integrated with conventional structural materials to serve as energy input devices or actuating elements in many engineering applications implementing intelligent material systems and structures concepts. In order to use the actuation mechanism produced by the integrated induced strain actuators efficiently, the mechanics of the mechanical interaction between the actuator and the host substructure must be understood and modeled accurately. A refined analytical model has been developed based on the plane stress formulation of the theory of elasticity for a surfacebonded induced strain actuator/beam substructure system. Closed-form solutions of the induced stress field were obtained in an approximate manner using the principle of stationary complementary energy. The model has also been extended to include the presence of adhesive bonding layers and applied external loads. The results of the current model were compared with those obtained by finite element analysis and the pin-force and Euler-Bernoulli models. It was shown that the current model is capable of describing the edge effects of the actuator on actuation force/moment transfer and interfacial shear and peeling stress distributions that the existing analytical models fail to describe. Good agreement was obtained between the current model and the finite element analysis in terms of predicting actuation force/moment transfer. The interfacial shear stress distribution obtained by the current model satisfies stress-free boundary conditions at the ends of the actuator, which the finite element model is not able to satisfy. The current model correctly describes the transfer of the actuation mechanism and the resulting interfacial stress distributions; thus, it can be used in designing integrated induced strain actuator/substructure systems. Moreover, a new induced strain actuator configuration, which includes inactive edges on the ends of the actuators, has been proposed to alleviate the intensity of the interfacial stresses. The effectiveness of the actuator on the interfacial stress alleviation was verified by the current analytical model and finite element analysis. It was shown that the proposed actuator configuration can significantly alleviate intensive interfacial shear and peeling stresses without sacrificing the effectiveness of the actuation mechanism. The chances of interfacial failure of the integrated structural system, fatigue failure in particular, can thus be reduced. / Ph. D.

This work investigates the potential of reducing stresses in the region of stress concentration by applied induced strains. A thin 30 inch square plate with a 1 inch diameter circular hole under uniaxial load was used for this investigation. This investigation considered first an ideal case with a few physical limitations for the purpose of probing the limits of active stress reduction. Applied induced strains were applied over the region A ≤ r ≤ 1.5A, where A is the radius of the hole. It was found that the axisymmetric applied induced strains could reduce the stress concentration factor (SCF) from 3 to 2. With non-axisymmetric applied induced strain distribution the SCF could be reduced to 1.45. Numerical optimizations based on finite element simulations were also carried out for a composite plate with a hole and similar reductions in stress concentration factors were obtained. Next, a more realistic case, consisting of bonded and embedded piezoelectric actuators was considered. It was found that partial-thickness actuators produce large radial stresses which erase any benefits associated with axisymmetric actuation. With non-axisymmetric actuation, the actuators with present technology limitations were found to be effective in reducing stress concentration factor for a fatigue load case. However, due to repetitive nature of the load, the energy expenditure may be large. For an extreme load case, actuators with present technology limitations were not very effective in reducing SCF. Actuators were needed to be placed over a larger area to achieve a larger reduction in SCF. Also, passive stiffening was found to be more effective in reducing stress concentration than bonded actuators with present technology limitations. / Ph. D.

Essa dissertação de mestrado é dedicada ao estudo, desenvolvimento e caracterização da resposta dinâmica de transdutores de deformação mecânica e de temperatura baseados em grades de Bragg inscritas em fibras ópticas (FBG). Como não se encontram referências diretas na literatura da área sobre a caracterização da resposta dinâmica de sensores de temperatura e deformação a FBG, percebeu-se a importância de realizar um trabalho com ênfase nesse aspecto. O desenvolvimento de transdutores FBG de deformação e de temperatura com resposta dinâmica rápida é de grande importância, já que as grades de Bragg são afetadas, de maneira intrínseca, simultaneamente pelas duas grandezas e que existe um amplo leque de aplicações em que uma delas, ou ambas, variam rapidamente. Nesses casos, diferenças em termos de tempos de resposta entre os sensores utilizados para medição de deformação e os usados para compensação de temperatura podem acarretar em erros significativos nas medidas, o que pode até inviabilizar o uso dos sensores a grades de Bragg em tais aplicações. Este trabalho apresenta um compêndio da teoria da tecnologia das FBG para aplicação em sensores ópticos de deformação e de temperatura. Buscando contribuir para o domínio das técnicas de fabricação de sensores a FBG no Brasil, também são apresentados os resultados experimentais da utilização de grades de Bragg inscritas em fibras ópticas fabricadas no laboratório da Subdivisão de Sensores (EFO-S), da Divisão de Fotônica do Instituto de Estudos Avançados (IEAv) do Comando-Geral de Tecnologia Aeroespacial (CTA), como elementos sensores em ensaios de deformação e de temperatura. Os resultados de caracterizações, tanto de FBG produzidas no IEAv quanto de sensores de deformação e de temperatura comerciais das empresas Micron Optics e Fiber Sensing, foram obtidos por meio de três interrogadores diferentes e são comparados e apresentados neste trabalho. Em uma análise realizada dos resultados apresentados de sensores a FBG, utilizados para medição de temperatura e de deformação mecânica em alguns arranjos experimentais, foram observados comportamentos dinâmicos não lineares que apresentam-se como um obstáculos a serem vencidos para a viabilização da aplicação desta técnica à medição desses parâmetros quando os mesmos são rapidamente variáveis. / This dissertation is devoted to the study, development and characterization of the dynamic response of mechanical strain and temperature transducers based on Bragg gratings inscribed in optical fibers (FBG). Since there are no direct references in the literature on the characterization of the dynamic response of FBG based temperature and strain sensors, it was realized the importance of conducting a study with emphasis on this aspect. The development of FBG strain and temperature transducers with fast dynamic response is of great importance, since the Bragg gratings are intrinsically and simultaneously affected by the two quantities and there is a wide range of applications in which one or both quantities vary rapidly. In such cases, differences in response times between the sensors used for measurement of strain and used for temperature compensation can result in significant errors, which may even preclude the use of FBG sensors in such applications. This work presents a compendium of the theory related to FBG technology for application in optical strain and temperature sensors. Seeking to master the techniques of manufacture of the FBG sensors in Brazil, experimental results from the use of FBG manufactured in the laboratory of Sensors Subdivision (EFO-S), of Photonics Division of Institute of Advanced Studies (IEAv) of General Command for Aerospace Technology (CTA) as sensor elements in strain and temperature trials are also presented. The results of both characterizations, of FBG produced in IEAv and strain and temperature commercial sensors, produced by Micron Optics and Fiber Sensing manufacturers, were obtained from three different interrogators and are compared and presented in this paper. In an analysis of the results of FBG sensors used for measuring temperature and mechanical deformation in some experimental arrangements, nonlinear dynamic behaviors were observed. Such behaviors present themselves as an obstacle to be overcome to achieve the feasibility of applying this technique to measurement of these parameters when they are rapidly changing.

Essa dissertação de mestrado é dedicada ao estudo, desenvolvimento e caracterização da resposta dinâmica de transdutores de deformação mecânica e de temperatura baseados em grades de Bragg inscritas em fibras ópticas (FBG). Como não se encontram referências diretas na literatura da área sobre a caracterização da resposta dinâmica de sensores de temperatura e deformação a FBG, percebeu-se a importância de realizar um trabalho com ênfase nesse aspecto. O desenvolvimento de transdutores FBG de deformação e de temperatura com resposta dinâmica rápida é de grande importância, já que as grades de Bragg são afetadas, de maneira intrínseca, simultaneamente pelas duas grandezas e que existe um amplo leque de aplicações em que uma delas, ou ambas, variam rapidamente. Nesses casos, diferenças em termos de tempos de resposta entre os sensores utilizados para medição de deformação e os usados para compensação de temperatura podem acarretar em erros significativos nas medidas, o que pode até inviabilizar o uso dos sensores a grades de Bragg em tais aplicações. Este trabalho apresenta um compêndio da teoria da tecnologia das FBG para aplicação em sensores ópticos de deformação e de temperatura. Buscando contribuir para o domínio das técnicas de fabricação de sensores a FBG no Brasil, também são apresentados os resultados experimentais da utilização de grades de Bragg inscritas em fibras ópticas fabricadas no laboratório da Subdivisão de Sensores (EFO-S), da Divisão de Fotônica do Instituto de Estudos Avançados (IEAv) do Comando-Geral de Tecnologia Aeroespacial (CTA), como elementos sensores em ensaios de deformação e de temperatura. Os resultados de caracterizações, tanto de FBG produzidas no IEAv quanto de sensores de deformação e de temperatura comerciais das empresas Micron Optics e Fiber Sensing, foram obtidos por meio de três interrogadores diferentes e são comparados e apresentados neste trabalho. Em uma análise realizada dos resultados apresentados de sensores a FBG, utilizados para medição de temperatura e de deformação mecânica em alguns arranjos experimentais, foram observados comportamentos dinâmicos não lineares que apresentam-se como um obstáculos a serem vencidos para a viabilização da aplicação desta técnica à medição desses parâmetros quando os mesmos são rapidamente variáveis. / This dissertation is devoted to the study, development and characterization of the dynamic response of mechanical strain and temperature transducers based on Bragg gratings inscribed in optical fibers (FBG). Since there are no direct references in the literature on the characterization of the dynamic response of FBG based temperature and strain sensors, it was realized the importance of conducting a study with emphasis on this aspect. The development of FBG strain and temperature transducers with fast dynamic response is of great importance, since the Bragg gratings are intrinsically and simultaneously affected by the two quantities and there is a wide range of applications in which one or both quantities vary rapidly. In such cases, differences in response times between the sensors used for measurement of strain and used for temperature compensation can result in significant errors, which may even preclude the use of FBG sensors in such applications. This work presents a compendium of the theory related to FBG technology for application in optical strain and temperature sensors. Seeking to master the techniques of manufacture of the FBG sensors in Brazil, experimental results from the use of FBG manufactured in the laboratory of Sensors Subdivision (EFO-S), of Photonics Division of Institute of Advanced Studies (IEAv) of General Command for Aerospace Technology (CTA) as sensor elements in strain and temperature trials are also presented. The results of both characterizations, of FBG produced in IEAv and strain and temperature commercial sensors, produced by Micron Optics and Fiber Sensing manufacturers, were obtained from three different interrogators and are compared and presented in this paper. In an analysis of the results of FBG sensors used for measuring temperature and mechanical deformation in some experimental arrangements, nonlinear dynamic behaviors were observed. Such behaviors present themselves as an obstacle to be overcome to achieve the feasibility of applying this technique to measurement of these parameters when they are rapidly changing.

Made available in DSpace on 2017-07-10T17:11:52Z (GMT). No. of bitstreams: 1 dissert Final Marcel Araujo.pdf: 10392408 bytes, checksum: 3344b21a2f98d64347dd0aea895a4444 (MD5) Previous issue date: 2013-03-01 / The use of piezoelectric devices to harvest vibration energy has found applications in several areas, especially in structural health monitoring, either to recharge batteries or to directly feed sensors and also electronic devices. In general, the practical use of the energy converted by these devices requires, first, converting the alternating current (AC) produced to direct current (DC). This is normally done by using rectifier circuits. However, modeling the harvesting system, usually a PZT sensor bonded on a cantilever micro-beam and coupled to a rectifier circuit, using the same software package is pointed out by some authors as a drawback to overcome, due to its multidisciplinary requirements, involving topics of both mechanical and electrical engineering. In this sense, the main goal of this dissertation is to describe a comprehensive and simple modeling strategy, which considers a single computational platform and, simultaneously, account for both the electromechanical model of a clamped piezoelectric beam and the practical energy harvesting circuit, seeking ways to facilitate the analysis and design of energy harvesting systems. Numerical simulations and experimental tests are performed to illustrate the proposed approach, considering a full-wave diode bridge as the non-controlled rectifier circuit and a resistive load, which are directly connected to the cantilevered piezoelectric beam. Additionally, experimental tests carried out with a commercial harvesting system are presented, aiming to characterize and compare its performance with a full-wave diode bridge and a resistive circuit, both developed by the author. A single degree of freedom model of this system is also presented. The results showed that the model is suitable to perform simulations of systemshaving the characteristics described in this dissertation and confirmed the need of using active circuits to better use the produced energy. / A utilização de dispositivos piezelétricos para reaproveitamento de energia vibratória tem en- contrado aplicações em várias áreas, sobretudo em monitoramento de integridade estrutural, seja para recarregar baterias ou alimentar diretamente sensores e outros dispositivos eletrôni- cos. Em geral, o uso prático da energia convertida por estes transdutores requer, primeiramente, a transformação da corrente alternada (CA) produzida em corrente contínua (CC). Isto é fre- quentemente obtido por meio da utilização de circuitos retificadores. Entretanto, utilizar o mesmo pacote de software para modelar sistemas de energy harvesting, geralmente compostos por um sensor piezelétrico acoplado em uma microviga e conectados a um circuito retificador, é apontado por alguns autores como um grande desafio a ser superado, pois necessita de requisi- tos multidisciplinares que incluem tópicos de engenharia elétrica e mecânica. Neste sentido, o principal objetivo deste trabalho é apresentar uma estratégia de modelagem simples, que utilize apenas uma plataforma computacional e considere, simultaneamente, os modelos de uma viga piezelétrica e um circuito prático de extração/armazenamento de energia, buscando meios de facilitar a análise e o projeto de sistemas de energy harvesting. Simulações numéricas e testes experimentais são realizados para ilustrar a abordagem proposta, considerando um circuito retificador de onda completa e uma carga resistiva conectados diretamente a uma viga piezelétrica sob condição engastada-livre. Além disso, são apresentados testes experimentais realizados com um sistema comercial de energy harvesting visando caracterizar e comparar seu desempenho frente aos circuitos retificadores de onda completa e resistivo, ambos confeccionados pelo autor. Um modelo de um grau de liberdade deste sistema também é apresentado. Os resultados mostraram que o modelo é adequado para realizar simulações de sistemas que possuam as características descritas neste trabalho e comprovaram a necessidade de se utilizar um circuito ativo para se ter um melhor reaproveitamento da energia gerada.

Resumo: Este trabalho tem como propósito utilizar técnicas de controle robusto para atenuação ativa de vibração mecânica em estruturas acopladas a atuadores e sensores piezelétricos. Os controladores são projetados segundo o enfoque de otimização convexa, com os requisitos envolvendo desigualdades matriciais lineares (LMIs). A proposta é ilustrar duas sínteses diferentes de realimentação via LMIs. A primeira é o projeto de controladores por realimentação de estados, estimados por um observador, considerando incertezas paramétricas do tipo politópicas. A segunda metodologia é baseada no controle H8 via realimentação do sinal de saída, considerando incertezas dinâmicas limitadas por norma. Os sensores/atuadores são posicionados em pontos ótimos utilizando-se a norma H8 como índice de desempenho. Os modelos matemáticos utilizados na síntese dos controladores foram obtidos a partir do método dos elementos finitos considerando o acoplamento eletromecânico entre os atuadores/sensores e a estrutura base ou a partir de métodos de identificação. Neste contexto, este trabalho também discute e exemplifica o algoritmo de realização de autosistemas (ERA). Três exemplos são solucionados para exemplificar a metodologia implementada: uma estrutura tipo placa, uma viga engastada-livre e a supressão ativa de flutter em um aerofólio 2-D, problema de grande interesse na indústria aeronáutica. Os resultados mostraram uma significante atenuação da vibração estrutural na faixa de freqüência de interesse e o atendimento dos requisitos impostos na fase de projeto. / Abstract: The proposal of this work is to use robust control techniques in order to suppress mechanical vibration in structures with pieozoelectric sensors and actuators coupled. The controllers are designed by convex optimization and the constraints are dealt through linear matrix inequalities (LMIs) frameworks. Two different methodologies to feedback the system by using LMIs are explained. The first one is the observer-based state-feedback considering polytopic uncertainties. The second one is the H output feedback control considering norm-bound uncertainties. The sensors/actuators are located in optimal placements by using H norm as performance index. The mathematical models used in the controller design were obtained by finite element methods considering eletromechanical effects between the host structure and piezoelectric sensors/actuators patches or by using identification methods. In this sense, it is also discussed the eigensystem realization algorithm (ERA). Three different applications are proposed and solved in order to illustrate the applicability of the methodology: a cantilever plate; a cantilever beam; and an active flutter suppression in a 2-D airfoil, a problem of considered interest in the aeronautic industry. The results showed the vibration suppression in the bandwidth of interest when submited to the requirements imposed by practical situations. / Orientador: Vicente Lopes Junior / Coorientador: Edvaldo Assunção / Banca: Vicente Lopes Junior / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Edilson Hiroshi Tamai / Mestre