Shape control of a structure with distributed piezoelectric actuators can be achieved through optimally selecting the loci, shapes and sizes of the piezoelectric actuators and choosing the electric fields applied to the actuators. Shape control can be categorised as either static or dynamic shape control. Whether it is a transient or gradual change, static or dynamic shape control, both aim to determine the loci, sizes, and shapes of piezoelectric actuators, and the applied voltages such that a desired structural shape is achieved effectively. This thesis is primarily concerned with establishing a finite element formulation for the general smart laminated composite plate structure, which is capable to analyse static and dynamic deformation using non-rectangular elements. The mechanical deformation of the smart composite plate is modelled using a third order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation for static and dynamics analysis is verified by comparing with available numerical results. Selected experiments have also been conducted to measure structural deformation and the experimental results are used to correlate with those of the finite element formulation for static analysis. In addition, the Linear Least Square (LLS) method is employed to study the effect of different piezoelectric actuator patch pattern on the results of error function, which is the least square error between the calculated and desired structural shapes in static structural shape control. The second issue of this thesis deals with piezoelectric actuator design optimisation (PADO) for quasi-static shape control by finding the applied voltage and the configuration of piezoelectric actuator patch to minimise error function, whereas the piezoelectric actuator configuration is defined based on the optimisation technique of altering nodal coordinates (size/shape optimisation) or eliminating inefficient elements in a structural mesh (topology optimisation). Several shape control algorithms are developed to improve the structural shape control by reducing the error function. Further development of the GA-based voltage and piezoelectric actuator design optimisation method includes the constraint handling, where the error function can be optimised subjected to energy consumption or other way around. The numerical examples are presented in order to verify that the proposed algorithms are applicable to quasi-static shape control based on voltage and piezoelectric actuator design optimisation (PADO) in terms of minimising the error function. The third issue is to use the present finite element formulation for a modal shape control and for controlling resonant vibration of smart composite plate structures. The controlled resonant vibration formulation is developed. Modal analysis and LLS methods are also employed to optimise the applied voltage to piezoelectric actuators for achieving the modal shapes. The Newmark direct time integration method is used to study harmonic excitation of smart structures. Numerical results are presented to induce harmonic vibration of structure with controlled magnitude via adjusting the damping and to verify the controlled resonant vibration formulation.

Shape control of a structure with distributed piezoelectric actuators can be achieved through optimally selecting the loci, shapes and sizes of the piezoelectric actuators and choosing the electric fields applied to the actuators. Shape control can be categorised as either static or dynamic shape control. Whether it is a transient or gradual change, static or dynamic shape control, both aim to determine the loci, sizes, and shapes of piezoelectric actuators, and the applied voltages such that a desired structural shape is achieved effectively. This thesis is primarily concerned with establishing a finite element formulation for the general smart laminated composite plate structure, which is capable to analyse static and dynamic deformation using non-rectangular elements. The mechanical deformation of the smart composite plate is modelled using a third order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation for static and dynamics analysis is verified by comparing with available numerical results. Selected experiments have also been conducted to measure structural deformation and the experimental results are used to correlate with those of the finite element formulation for static analysis. In addition, the Linear Least Square (LLS) method is employed to study the effect of different piezoelectric actuator patch pattern on the results of error function, which is the least square error between the calculated and desired structural shapes in static structural shape control. The second issue of this thesis deals with piezoelectric actuator design optimisation (PADO) for quasi-static shape control by finding the applied voltage and the configuration of piezoelectric actuator patch to minimise error function, whereas the piezoelectric actuator configuration is defined based on the optimisation technique of altering nodal coordinates (size/shape optimisation) or eliminating inefficient elements in a structural mesh (topology optimisation). Several shape control algorithms are developed to improve the structural shape control by reducing the error function. Further development of the GA-based voltage and piezoelectric actuator design optimisation method includes the constraint handling, where the error function can be optimised subjected to energy consumption or other way around. The numerical examples are presented in order to verify that the proposed algorithms are applicable to quasi-static shape control based on voltage and piezoelectric actuator design optimisation (PADO) in terms of minimising the error function. The third issue is to use the present finite element formulation for a modal shape control and for controlling resonant vibration of smart composite plate structures. The controlled resonant vibration formulation is developed. Modal analysis and LLS methods are also employed to optimise the applied voltage to piezoelectric actuators for achieving the modal shapes. The Newmark direct time integration method is used to study harmonic excitation of smart structures. Numerical results are presented to induce harmonic vibration of structure with controlled magnitude via adjusting the damping and to verify the controlled resonant vibration formulation.

Thesis (Ph. D.)--Auburn University. / Abstract. Vita. Includes bibliographical references (p. 100-106).

The use of piezoelectric materials for actuation, and vibration suppression of thin beams, is the subject of study in this doctoral thesis. The initial focus is set on reducing beam vibrations with resistively shunted piezoelectric patches, where the converted electrical energy is dissipated by the resistor to give an additional damping. The amount of additional damping achieved depends on the value of shunted resistor, the dimensions of the piezoelectric, and its location on the substructure. Hence, the resistively shunted piezoelectric-beam was modelled to determine the optimal values, and to examine its dynamics. A multi-modal model was derived based on the Euler-Bernoulli beam theory, and a reduced non-dimensionalized transfer function was obtained from the multi-modal model. The presented model was derived from assumptions which aptly describe the dynamics of the resistively shunted piezoelectric-beam. The aptness of the presented model in representing the system, over the existing models, was evident from the comparison of the analytical predictions with the existing experimental data. With the model derived, the second part of the work deals with determining the value of resistance which would yield maximum amplitude attenuation (referred as the optimal resistance value). A method for obtaining the optimal resistance value from the analytical model, based on the presence of a fixed-point in the amplitude response, exists in the literature. But, this method cannot be used on the presented analytical model, as it includes the base-damping of the structure. Hence, a different approach was adopted to determine the optimal resistance from the analytical model. Analytical results were also validated with experimental results from a cantilever piezoelectric-beam. The amplitude plots of the first, second, and third modes of the piezoelectric-beam exhibited a softening e ect, indicating a non-linear behaviour of the piezoelectric patches. Hence, a non-linear constitutive equation was required to describe the behaviour of the piezoelectric patches. In the third part of the work, a two-step experimental procedure was devised to construct the non-linear constitutive equation of the piezoelectric actuators. In the first step, the piezoelectric patches were short circuited and a family of displacement curves were obtained for the first, second and third modes of the piezoelectric-beam by base excitation. The pro le of backbone curves from these plots were used to identify the type of non-linear terms required to describe the mechanical domain. In the second step, voltage excitation was used to obtain a similar set of displacement curves. A comparison of the profile of the backbone curves, of the displacement frequency response plot, from the voltage excited data with those from the base excited data, lead to the identification of the non-linear electromechanical coupling term. The constitutive equation, which accounts for the non-linear nature, of the piezoelectric actuator contains (apart from the linear terms) a quadratic strain term, a cubic strain term, and a term with the product of cubic strain and electric field.

Trata do desenvolvimento de um porta-ferramenta translativo (PFT). Objetiva o microposicionamento relativo ferramenta/peça durante a usinagem de ultraprecisão, para atender à tolerâncias nanométricas. Define esse microposicionamento com o emprego de atuador piezelétrico. Mostra alguns aspectos de projeto aplicados à engenharia de precisão que foram usados no desenvolvimento do PFT. Relata as técnicas de controle aplicadas como PID e compensador por atraso de fase. Realiza uma análise para verificação dos modos de vibrar do PFT, identificando assim as freqüências naturais do sistema. Apresenta um modelo ideal, ou seja, todos os componentes foram fabricados e montados para a realização dos testes. Propõe que a estratégia de controle seja baseada em processar sinais adquiridos ao longo do microposicionamento da ferramenta para identificar a condição de posicionamento relativo ferramenta/peça e obter informações que foram posteriormente usadas em um controlador PID, para realimentação de posição. Conclui com a avaliação e testes experimentais de deslocamento da ferramenta de corte, até 25 &#956m; com freqüência, até 10 Hz, realizados com o PFT projetado. / This work deals with the development of a tool post (PFT) for the micropositioning of a tool during ultraprecision machining in the nanometric range. Micropositioning employing piezoelectric actuators is defined. Precision engineering designs aspects applied to the development of the PFT are discussed. Control techniques such as PID and phase-lag compensator are addressed. A computer simulation for the verification of the vibrating modes of the PFT, with the simultaneous identification of the natural frequencies is carried out. An ideal model - all components will be manufactured and assembled - is presented. A control strategy based on the processing of signals acquired during the micropositioning of the tool to identify the positioning condition and to obtain information to be used by a PID controller is proposed. Experimental tests are performed with displacement of the tool, up to 25 &#956m, with frequency, up to 10 Hz.

The aim of this thesis is to show that it is possible to damp mechanical vibrations in a given frame, constituted by Euler beam governed by the equations of an elastica, by means of piezoelectric actuators glued on every beam and interconnected each other via electrical networks.Since we believe that the most efficient way to damp mechanical vibrations by means of electrical networks, is to realize a strong modal coupling between the electrical and the mechanical motion, we will synthesize a distributed circuit analog to the Euler beam.We will approach this synthesis problem following the black box approach to mechanical systems, studied by many engineers and scientists during the 1940's in an attempt to design analog computers.It will be shown that it is possible to obtain a quick energy exchange between its mechanical and electrical forms, using available piezoelectric actuators.Finally we will study a numerical simulation for the damping of transverse vibrations of a beam clamped at both ends. / Master of Science

No description available.

With increasing advancement in material science and computational power of current computers that allows us to analyze high dimensional systems, very light and large structures are being designed and built for aerospace applications. One example is a reflector of a space telescope that is made of membrane structures. These reflectors are light and foldable which makes the shipment easy and cheaper unlike traditional reflectors made of glass or other heavy materials. However, one of the disadvantages of membranes is that they are very sensitive to external changes, such as thermal load or maneuvering of the space telescope. These effects create vibrations that dramatically affect the performance of the reflector. To overcome vibrations in membranes, in this work, piezoelectric actuators are used to develop distributed controllers for membranes. These actuators generate bending effects to suppress the vibration. The actuators attached to a membrane are relatively thick which makes the system heterogeneous; thus, an analytical solution cannot be obtained to solve the partial differential equation of the system. Therefore, the Finite Element Model is applied to obtain an approximate solution for the membrane actuator system. Another difficulty that arises with very flexible large structures is the dimension of the discretized system. To obtain an accurate result, the system needs to be discretized using smaller segments which makes the dimension of the system very high. This issue will persist as long as the improving technology will allow increasingly complex and large systems to be designed and built. To deal with this difficulty, the analysis of the system and controller development to suppress the vibration are carried out using vector second order form as an alternative to vector first order form. In vector second order form, the number of equations that need to be solved are half of the number equations in vector first order form. Analyzing the system for control characteristics such as stability, controllability and observability is a key step that needs to be carried out before developing a controller. This analysis determines what kind of system is being modeled and the appropriate approach for controller development. Therefore, accuracy of the system analysis is very crucial. The results of the system analysis using vector second order form and vector first order form show the computational advantages of using vector second order form. Using similar concepts, LQR and LQG controllers, that are developed to suppress the vibration, are derived using vector second order form. To develop a controller using vector second order form, two different approaches are used. One is reducing the size of the Algebraic Riccati Equation to half by partitioning the solution matrix. The other approach is using the Hamiltonian method directly in vector second order form. Controllers are developed using both approaches and compared to each other. Some simple solutions for special cases are derived for vector second order form using the reduced Algebraic Riccati Equation. The advantages and drawbacks of both approaches are explained through examples. System analysis and controller applications are carried out for a square membrane system with four actuators. Two different systems with different actuator locations are analyzed. One system has the actuators at the corners of the membrane, the other has the actuators away from the corners. The structural and control effect of actuator locations are demonstrated with mode shapes and simulations. The results of the controller applications and the comparison of the vector first order form with the vector second order form demonstrate the efficacy of the controllers. / Ph. D.

Trata do desenvolvimento de um controlador Proporcional-Integral-Derivativo (PID) para uma Mesa Angular Rotativa (MAR) destinada à usinagem de ultraprecisão. O sistema de controle tem como objetivo efetuar posicionamento angular de alta resolução e repetibilidade antes e durante a usinagem de ultraprecisão, propiciando fabricar peças complexas através de torneamento. A MAR faz uso de elementos como mancais de flexão, atuadores piezelétricos, juntamente com o sistema de controle PID. A estratégia de controle é baseada na aquisição de dados na plataforma de desenvolvimento LabVIEW®, para gerar curvas tensão de saída do tesatronic versus deslocamento da MAR e no processamento dos sinais adquiridos ao longo do microposicionamento da MAR em tempo real para realimentação de posição. Constatou-se que o sistema suporta deslocamentos da MAR correspondendo a expansão do atuador piezelétrico de até 24 µm com freqüência de acionamento de até 3 Hz. O uso de filtro Chebyshev provocou atraso na resposta e forte instabilidade no sistema. Conclui-se que para a melhora do desempenho do sistema em termos de freqüência pode ser conseguida através do uso de filtro do tipo FIR (Finite Impulse Response). / A Micro Tilt Stage (MTS) was developed in the Precision Engineering Laboratory (University of São Paulo) to be used in commercial diamond turning machines. The MTS has the aim of positioning workpieces angularly with high resolution and repeatability before and during ultraprecision machining. The use of flexural bearings and piezoelectric actuators together with a PID control system provided improved dynamic performance. The control strategy is based on data acquisition using LabView to create standard curves and perform the correction of positioning errors. Experimental tests are performed with displacement of the (MTS), up to 24 µm, with frequency, up to 3 Hz. The use of a Chebyshev filter caused a delay and a strong instability in the system. In conclusion, in order to improve the performance of the system in terms of frequency, the use of a FIR filter (Finite Impulse Response) may be indicated.

As bombas de fluxo, além das aplicações clássicas em Engenharia, são instrumentos importantes em áreas como a Bioengenharia, seja para o bombeamento de sangue ou dosagem de reagentes e medicamentos, e na área de refrigeração de equipamentos eletrônicos. Muitos dos novos princípios aplicados no desenvolvimento desse tipo de bomba de fluxo baseiam-se no uso de atuadores piezelétricos. Esses atuadores apresentam certas vantagens em relação a outros tipos tradicionalmente utilizados, como maior potencial de miniaturização, menor geração de ruídos e número reduzido de partes móveis. Entre os vários tipos de bombas de fluxo piezelétricas destacam-se as baseadas nos movimentos ondulatórios e oscilatórios, como o nadar dos peixes. É bem conhecido que os peixes ao nadarem não provocam a morte de micro-organismos ao seu redor, o que torna esse princípio bem promissor para as aplicações em Biotecnologia, por exemplo. Assim, o presente trabalho de mestrado dedica-se ao estudo de novas configurações de atuadores piezelétricos bilaminares associados em paralelo e série para bombeamento de líquidos através do princípio oscilatório, a fim de se obter maiores vazões ou pressões. O escopo deste projeto abrange, computacionalmente, análises estruturais de atuadores piezelétricos bilaminares e simulações do escoamento de fluido e, experimentalmente, construções de protótipos para validação de resultados. Inicialmente é investigado o comportamento de um único atuador piezelétrico bilaminar em fluido viscoso (água), a fim de se dominar o princípio de funcionamento proposto neste trabalho. Esse estudo serviu de referência para as configurações de atuadores em série e paralelo propostas. Espera-se que a configuração dos atuadores em paralelo apresente um ganho na vazão de saída, enquanto que a configuração dos atuadores em série apresente um ganho na pressão de saída. Ao longo desta dissertação são apresentadas a metodologia empregada e as discussões dos resultados obtidos, de forma a analisar o princípio proposto e os fenômenos físicos em questão. / Flow pumps, in addition to traditional applications in Engineering, are important tools in areas such as Bioengineering, applied to blood pumping, dosage of medicine and chemical reagents, and in the field of thermal management solutions for electronic devices. Many of the new principles in flow pumps development are based on the use of piezoelectric actuators. These actuators present some advantages in relation to other applied types, for example, miniaturization potential, lower noise generation and fewer numbers of moving parts. Flow pumps based on undulatory and oscillatory movements, such as fish swimming, stand out among the various types of piezoelectric flow pumps. It is well known that fish swimming does not cause the death of microorganisms, what makes this principle applicable in Biotechnology, for example. Thus, the objective of this work is to study parallel-cascade configurations of bimorph piezoelectric actuators for liquid pumping based on the oscillatory principle, in order to obtain higher flow rates and pressure. The scope of this work includes structural and analyses of bimorph piezoelectric actuators and fluid flow simulations, and construction of prototypes for result validation. First, it is investigated the behavior of a single bimorph piezoelectric actuator oscillating in viscous fluid (water) to better understand the working principle used in this work. The study of a single piezoelectric actuator was used as a reference for the other proposed parallel-cascade configurations of actuators. It is expected that parallel actuators achieve higher flow rates, while the series actuators achieve higher pressures. The methods employed are presented and the obtained results are discussed, analyzing the principle and the related physical phenomena.