Este trabalho apresenta o desenvolvimento de uma metodologia para a estimativa de funções de resposta em freqüência angulares (FRFAs). Trata-se de uma técnica que utiliza transdutores piezelétricos (PZT) do tipo bimorph para a medição da curvatura local da estrutura através do potencial elétrico induzido pela extensão e compressão do sensor. A partir da estimativa da curvatura, a rotação pode ser obtida diretamente através de várias técnicas de interpolação (polinomial, formas modais, etc). Apresenta-se a modelagem téorica da qual se deriva as equações que governam a dinâmica de estruturas uni-dimensionais, do tipo viga, e estruturas bidimensionais, do tipo placa, ambas isotrópicas, onde se incorpora o sensor bimorph. Modelos em elementos finitos foram propostos no intuito de avaliar a utilização destes sensores (bimorphs) aplicados à estimativa das FRFAs. Apresentam-se também resultados numéricos e experimentais considerando-se uma viga engastada-livre (cantilever) e resultados numéricos considerando-se uma placa simplesmente apoiada. Um algoritmo genético foi ainda desenvolvido no intuito de determinar a posição e dimensão ótimas dos bimorphs em estruturas do tipo viga. / The present work aims to perform the development of an attractive approach for accurate measurement of angular frequency response functions (AFRFs). It uses bimorph piezoceramic patches to measure the structure\'s local curvature through the measurement of the electric potential induced by the extension and compression of the patch\'s top and bottom stripes, respectively. From this curvature, rotation can be obtained directly by several interpolation techniques (single polynomial, modes basis). Theoretical modeling of the vibration incorporating piezoelectric bimorph sensor is presented and equations governing the dynamics for one-dimensional structures, like a beam, and for two-dimensional structures, like a plate, are derived for isotropic structures. Finite element model for the dynamic analysis were proposed to evaluate bimorphs patches applied to the measurement of angular FRFs. Numerical and experimental results are presented considering a cantilever beam and numerical results for a simply supported plate as tested structured. Also, in this work, a genetic algorithm was used as an adaptive heuristic search algorithm for optimal placement and sizing of the bimorph sensor into beam like structures.

Este trabalho apresenta o desenvolvimento de uma metodologia para a estimativa de funções de resposta em freqüência angulares (FRFAs). Trata-se de uma técnica que utiliza transdutores piezelétricos (PZT) do tipo bimorph para a medição da curvatura local da estrutura através do potencial elétrico induzido pela extensão e compressão do sensor. A partir da estimativa da curvatura, a rotação pode ser obtida diretamente através de várias técnicas de interpolação (polinomial, formas modais, etc). Apresenta-se a modelagem téorica da qual se deriva as equações que governam a dinâmica de estruturas uni-dimensionais, do tipo viga, e estruturas bidimensionais, do tipo placa, ambas isotrópicas, onde se incorpora o sensor bimorph. Modelos em elementos finitos foram propostos no intuito de avaliar a utilização destes sensores (bimorphs) aplicados à estimativa das FRFAs. Apresentam-se também resultados numéricos e experimentais considerando-se uma viga engastada-livre (cantilever) e resultados numéricos considerando-se uma placa simplesmente apoiada. Um algoritmo genético foi ainda desenvolvido no intuito de determinar a posição e dimensão ótimas dos bimorphs em estruturas do tipo viga. / The present work aims to perform the development of an attractive approach for accurate measurement of angular frequency response functions (AFRFs). It uses bimorph piezoceramic patches to measure the structure\'s local curvature through the measurement of the electric potential induced by the extension and compression of the patch\'s top and bottom stripes, respectively. From this curvature, rotation can be obtained directly by several interpolation techniques (single polynomial, modes basis). Theoretical modeling of the vibration incorporating piezoelectric bimorph sensor is presented and equations governing the dynamics for one-dimensional structures, like a beam, and for two-dimensional structures, like a plate, are derived for isotropic structures. Finite element model for the dynamic analysis were proposed to evaluate bimorphs patches applied to the measurement of angular FRFs. Numerical and experimental results are presented considering a cantilever beam and numerical results for a simply supported plate as tested structured. Also, in this work, a genetic algorithm was used as an adaptive heuristic search algorithm for optimal placement and sizing of the bimorph sensor into beam like structures.

Actuating a cantilever piezoelectric element over a frequency spectrum, the movement will show resonances and hysteresis behavior not present in the input signal. Excursion modeling and open loop control of a cantilever piezoelectric bimorph actuator was studied in this thesis, with the aim to enhance the actuator's movement to more accurately render audible input. This actuator has lower energy consumption and presents new possibilities for speaker design in constrained situations compared to conventional micro speaker technology. Much work has previously been done to model piezoelectric cantilever actuators below the first and second resonance frequency. This thesis describes a physical linear model and its modifications to render the eight first resonance frequencies below 20 kHz, as well as the model's performance in open loop control. This was performed on a single piezoelectric beam and a concept piezoelectric speaker. For the single piezoelectric beam the model was validated with fair overall result below 3 kHz. The model is suggested to have fair overall behavior up to 15 kHz. Above 15 kHz the experiments showed changed characteristics that were not modeled well. The open loop control had the intended behavior but severe resonances and physical constraints made the open loop control ineffective to enhance the sound rendering. Two different approaches were used for trying to improve the sound rendering based on an excursion model. These approaches did not generate useful methods but present viable input to future work with this type of speaker structure, for reducing disharmonics and creating a physical design tool for sound simulation. For the concept piezoelectric speaker, due to difficulties in measuring excursion, the model could not be validated. This made the approaches for enhancing the sound rendering ineffective. However, it can be concluded from the concept speaker that the cantilever piezoelectric speaker technology has qualities that could compete with the conventional micro speaker technology. Challenges remain in electric hardware, actuator configuration and acoustic design as well as in fine tuned signal processing for the concept speaker to become a competitive product.

Piezoelectrics offer high actuation authority and sensing over a wide range of frequencies. A Macro-Fiber Composite is a type of piezoelectric device that offers structural flexibility and high actuation authority. A challenge with piezoelectric actuators is that they require high voltage input; however the low power consumption allows for relatively lightweight electronic components. Another challenge, for piezoelectric actuated aerodynamic surfaces, is found in operating a relatively compliant, thin structure (desirable for piezoceramic actuators) in situations where there are relatively high external (aerodynamic) forces. Establishing an aeroelastic configuration that is stiff enough to prevent flutter and divergence, but compliant enough to allow the range of available motion is the central challenge in developing a piezocomposite airfoil. The research proposed here is to analyze and implement novel electronic circuits and structural concepts that address these two challenges. Here, a detailed theoretical and experimental analysis of the aerodynamic and electromechanical systems that are necessary for a practical implementation of a piezocomposite airfoil is presented. First, the electromechanical response of Macro-Fiber Composite based unimorph and bimorph structures is analyzed. A distributed parameter electromechanical model is presented for interdigitated piezocomposite unimorph actuators. Necessary structural features that result in large electrically induced deformations are identified theoretically and verified experimentally. A novel, lightweight electrical circuitry is proposed and implemented to enable the peak-to-peak actuation of Macro-Fiber Composite bimorph devices with asymmetric voltage range. Next, two novel concepts of supporting the piezoelectric material are proposed to form two types of variable-camber aerodynamic surfaces. The first concept, a simply-supported thin bimorph airfoil, can take advantage of aerodynamic loads to reduce control input moments and increase control effectiveness. The structural boundary conditions of the design are optimized by solving a coupled fluid-structure interaction problem by using a structural finite element method and a panel method based on the potential flow theory for fluids. The second concept is a variable-camber thick airfoil with two cascading bimorphs and a compliant box mechanism. Using the structural and aerodynamic theoretical analysis, both variable-camber airfoil concepts are fabricated and successfully implemented on an experimental ducted-fan vehicle. A custom, fully automated low-speed wind tunnel and a load balance is designed and fabricated for experimental validation. The airfoils are evaluated in the wind tunnel for their two-dimensional lift and drag coefficients at low Reynolds number flow. The effects of piezoelectric hysteresis are identified. In addition to the shape control application, low Reynolds number flow control is examined using the cascading bimorph variable-camber airfoil. Unimorph type actuators are proposed for flow control in two unique concepts. Several electromechanical excitation modes are identified that result in the delay of laminar separation bubble and improvement of lift. Periodic excitation to the flow near the leading edge of the airfoil is used as the flow control method. The effects of amplitude, frequency and spanwise distribution of excitation are determined experimentally using the wind tunnel setup. Finally, the effects of piezoelectric hysteresis nonlinearity are identified for Macro-Fiber Composite bimorphs. The hysteresis is modeled for open-loop response using a phenomenological classical Preisach model. The classical Preisach model is capable of predicting the hysteresis observed in 1) two cantilevered bimorph beams, 2) the simply-supported thin airfoil, and 3) the cascading bimorph thick airfoil. / Ph. D.

Flow control can lead to saving millions of dollars in fuel costs each year by making an aircraft more efficient. Synthetic jets, a device for active flow control, operate by introducing small amounts of energy locally to achieve non-local changes in the flow field with large performance gains. These devices consist of a cavity with an oscillating diaphragm that divides it, into active and passive sides. The active side has a small opening where a jet is formed, whereas and the passive side does not directly participate in the fluidic jet.Research has shown that the synthetic jet behavior is dependent on the diaphragm and the cavity design hence, the focus of this work. The performance of the synthetic jet is studied under various factors related to the diaphragm and the cavity geometry. Four diaphragms, manufactured from piezoelectric composites, were selected for this study, Bimorph, Thunder®, Lipca and RFD. The overall factors considered are the driving signals, voltage, frequency, cavity height, orifice size, and passive cavity pressure. Using the average maximum jet velocity as the response variable, these factors are individually studied for each actuator and statistical analysis tools were used to select the relevant factors in the response variable. For all diaphragms, the driving signal was found to be the most important factor, with the sawtooth signal producing significantly higher velocities than the sine signal. Cavity dimensions also proved to be relevant factors when considering the designing of a synthetic jet actuator. The cavities with the smaller orifice produced lower velocities than those with larger orifices and the cavities with smaller volumes followed the same trend. Although there exist a relationship between cavity height and orifice size, the orifice size appears as the dominant factor.Driving frequency of the diaphragm was the only common factor to all diaphragms studied that was not statistically significant having a small effect on jet velocity. However along with waveform, it had a combined effect on jet velocity for all actuators. With the sawtooth signal, the velocity remained constant after a particular low frequency, thus indicating that the synthetic jet cavity could be saturated and the flow choked. No such saturation point was reached with the sine signal, for the frequencies tested. Passive cavity pressure seemed to have a positive effect on the jet velocity up to a particular pressure characteristic of the diaphragm, beyond which the pressure had an adverse effect. For Thunder® and Lipca, the passive cavity pressure that produced a peak was measured at approximately 20 and 18kPa respectively independent of the waveform utilized. For a Bimorph and RFD, this effect was not observed.Linear models for all actuators with the factors found to be statistically significant were developed. These models should lead to further design improvements of synthetic jets.

The degradation of astronomical images caused by atmospheric turbulence will be much more severe in the next generation of terrestrial telescopes and its compensation will require deformable mirrors with up to tens-of-thousands of actuators. Current designs for these correctors consist of scaling up the proven technologies of flexible optical plates deformed under the out-of-plane action of linear actuators. This approach will lead to an exponential growth of cost with the number of actuators, and in very complex mechanisms. This thesis proposes a new concept of optical correction which is modular, robust, lightweight and low-cost and is based on the bimorph in-plane actuation. The adaptive mirror consists of segmented identical hexagonal bimorph mirrors allowing to indefinitely increase the degree of correction while maintaining the first mechanical resonance at the level of a single segment and showing an increase in price only proportional to the number of segments. Each bimorph segment can be mass-produced by simply screen-printing an array of thin piezoelectric patches onto a silicon wafer resulting in very compact and lightweight modules and at a price essentially independent from the number of actuators. The controlled deformation of a screen-printed bimorph mirror was experimentally achieved with meaningful optical shapes and appropriate amplitudes; its capability for compensating turbulence was evaluated numerically. The generation of continuous surfaces by an assembly of these mirrors was numerically simulated and a demonstrator of concept consisting of 3 segments was constructed.

In high density magnetic hard disk drives, both fast track seeking and extremely accurate positioning of the read/write head are required. A new piezoelectric microactuator with transverse and lateral control of the head positioning system for high density hard disk drives is proposed. First, the structure of the new piezoelectric microactuator is illustrated. Design of the new microactuator is based on the axial deformation of piezoelectric elements for lateral motion and the bimorph actuation of piezoelectric elements for transverse motion. Next, a mathematical model of the microactuator system is defined. Static properties associated with the displacement of the system are evaluated and then dynamic system equations of the system are evaluated. Frequency response of the system is studied based on the dynamic system equations of the actuator system. Dynamic properties of the system with a variety of system parameters are evaluated. Finally, the controller design for the actuator is presented. Simulation results show that the new actuator achieves a maximum stroke of displacement of more than 0.2m with servo bandwidth of more than 5 kHz in the lateral direction and the flying height is decreased to less than 6 nm with resonance frequency of more than 100 kHz under the 0.5 % damping assumption. The new piezoelectric microactuator improves performance of high density hard disk drives by increasing servo bandwidth and decreasing flying height.

Abstract Many electrical devices already surround us in our everyday life. Some devices monitor car performance and traffic while others exist in handheld devices used by the general public. Electrical devices also control manufacturing processes and protect workers from exposure to hazardous working environment. All these devices require electricity to operate. This exponential growth of low power electronic devices in industry, healthcare, military, transportation and in portable personal devices has led to an urgent need for system integrated energy sources. Many energy harvesting technologies have been developed to serve as a power source in close proximity to the electrical device itself. Solar and magnetic energy harvesters are the most common solutions when conditions are suitable. A more recent technique, called piezoelectric energy harvesting, has raised significant interest among scientists and in industry. Through piezoelectric (ceramic) material mechanical energy can be harvested and converted to electrical energy. This method requires accurate analysis of the kinetic energy experienced by the piezoelectric material so that the mechanics can be suitably designed. At the same time the mechanical design has to protect the piezoelectric material from intense forces that might cause cracks, while still transmitting the kinetic energy efficiently. These requirements usually mean a specific energy harvest design for each ambient energy source at hand. This thesis is focused on energy harvesting from low frequency compressions using piezoelectric ceramic materials. The objective was to manufacture, measure and implement structures that could sustain the forces experienced under the heel of a foot and maximize the harvested energy amount and efficiency. Two different construction designs were developed and optimised with an iterative process. The kinetic energy impulse under the heel part of the foot was studied by measuring the electrical output of the harvester during walking and then analysed with modelling software. The results were used to create a walking profile for a computer controlled piston to study the input energy phase, speed and force influence on the amount of the harvested energy and the efficiency of the harvesting process. Finally, the functionality of the concept was tested in a real environment with an energy harvester inserted inside a running shoe. The developed harvester showed the highest energy density reported in this frequency region. / Tiivistelmä Monet elektroniset laitteet ympäröivät meitä jokapäiväisessä elämässä. Ne tarkkailevat auton toimintaa tai liikennettä ja toiset toimivat aina mukana kulkevissa kannettavissa laitteissa. Töissä ne valvovat valmistusprosesseja tai varoittavat työntekijöitä vaarallisista työolosuhteista. Kaikki nämä laitteet tarvitsevat sähköä toimiakseen. Pienitehoisten elektronisten laitteiden eksponentiaalinen kasvu teollisuudessa, terveyssektorilla, puolustusteollisuudessa, kulkuneuvoissa sekä kannettavassa kulutuselektroniikassa on johtanut suureen tarpeeseen kehittää järjestelmiin integroituja energialähteitä. Monia energiankeräystekniikoita on kehitetty toimimaan elektronisten laitteiden läheisyydessä. Aurinkopaneelit ja magneettiset energiankeräysmenetelmät ovat yleisimpiä ratkaisuja, jos olosuhteet antavat siihen mahdollisuuden. Pietsosähköinen energiankeräys on uudempi tekniikka, joka on herättänyt kasvavaa huomiota tutkimusyhteisössä sekä teollisuudessa. Pietsosähköisen materiaalin avulla mekaaninen energia voidaan muuntaa suoraan sähköiseksi energiaksi. Tässä tekniikassa kineettinen energia tulee analysoida tarkasti mekaniikka suunnittelua varten, jotta se saadaan kohdistettua tehokkaasti pietsosähköiseen materiaaliin. Lisäksi mekaniikan tulee suojata materiaalia voimilta, jotka voivat johtaa murtumiin. Näistä vaatimuksista johtuen jokainen ulkoinen energialähde vaatii yleensä yksilöllisen energiankeräysrakenteen. Tämä väitöstyö keskittyy pietsosähköisten keraamien hyödyntämiseen energiankeräyksessä matalataajuisista mekaanisista voimista. Tarkoituksena oli suunnitella, valmistaa, mitata ja asentaa rakenteita, jotka kestävät kantapäähän kohdistuvia voimia kävelyn ja juoksun aikana sekä maksimoida talteen saatava energia ja hyötysuhde. Kaksi erilaista rakennetta suunniteltiin, valmistettiin ja optimoitiin energiankeräystä varten. Kantapäähän kohdistuva kineettinen energia analysoitiin mallinnusohjelmistolla ja mittaamalla sähköinen vaste energiakeräys rakenteesta. Tuloksien avulla suunniteltiin kävelyprofiilia imitoiva mekaaninen männän liike, jonka avulla tutkittiin kohdistettavan voiman nopeuden, vaiheen ja suuruuden vaikutusta energiankeräyksen hyötysuhteeseen ja saatavaan tehoon. Viimeisenä energiankeräysrakenteen toimivuutta testattiin oikeassa ympäristössä asentamalla se juoksukenkään. Kehitetyllä pietsosähköisellä energiakeräimellä saavutettiin korkeimmat raportoidut energiatiheydet käytetyllä taajuusalueella.

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Flapping-wing micro air vehicle (MAV) is an emerging micro-robotic technology, which has several challenges toward its practical implementation. Inspired by insect flight, researchers have adopted bio-mimicking approach to accomplish its engineering model. There are several methods to synthesize such an electromechanical system. A piezoelectric actuator driven flapping mechanism, being voltage controlled, monolithic, and of solid state type exhibits greater potential than any conventional motor driven flapping wing mechanism at small scale. However, the demand for large tip deflection with constrained mass introduces several challenges in the design of such piezoelectric actuators for this application. The mass constraint restricts the geometry, but applying high electric field we can increase the tip deflection in a piezoelectric actuator. Here we have investigated performance of rectangular piezo-actuator at high electric field. The performance measuring attributes such as, the tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically calculated for the actuator at high electric field. The analytical results suggest that the performance of such an actuator can be improved by tailoring the geometry while keeping the mass and capacitance constant. Thereby, a tapered piezoelectric bimorph cantilever actuator can provide better electromechanical performance for out-of-plane deflection, compared to a rectangular piezoelectric bimorph of equal mass and capacitance. The constant capacitance provides facility to keep the electronic signal bandwidth unchanged. We have analytically presented improvement in block force and its corresponding output strain energy, energy density and energy effi- ciency with tapered geometry. We have quantitatively and comparatively shown the per- formance improvement. Then, we have considered a rigid extension of non-piezoelectric material at the tip of the piezo-actuator to increase the tip deflection. We have an- alytically investigated the effect of thick and thin rigid extension of non-piezoelectric material on the performance of this piezo-actuator. The formulation provides scope for multi-objective optimization for the actuator subjected to mechanical and electrical con- straints, and leads to the findings of some useful pareto optimal solutions. Piezoelectric materials are polarized in a certain direction. Driving a piezoelectric actuator by high electric field in a direction opposite to the polarized direction can destroy the piezo- electric property. Therefore, unipolar high electric field is recommended to drive such actuators. We have discussed the drawbacks of existing switching amplifier based piezo- electric drivers for flapping wing MAV application, and have suggested an active filter based voltage driver to operate a piezoelectric actuator in such cases. The active filter is designed to have a low pass bandwidth, and use Chebyshev polynomial to produce unipolar high voltage of low flapping frequency. Adjustment of flapping frequency by this voltage driver is compatible with radio control communication. To accomplish the flapping-wing mechanism, we have addressed a compatible dis- tributed compliant mechanism, which acts like a transmission between the flapping wing of a micro air vehicle and the laminated piezoelectric actuator, discussed above. The mechanism takes translational deflection at its input from the piezoelectric actuator and provides angular deflection at its output, which causes flapping. The feasibility of the mechanism is investigated by using spring-lever (SL) model. A basic design of the com- pliant mechanism is obtained by topology optimization, and the final mechanism is pro- totyped using VeroWhitePlus RGD835 material with an Objet Connex 3D printer. We made a bench-top experimental setup and demonstrated the flapping motion by actuating the distributed compliant mechanism with a piezoelectric bimorph actuator.