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Exploiting new advanced structures and electromechanical systems, e. g. , adaptive structures, high-precision systems, micro electromechanical systems, distributed sensors/actuators, precision manipulation and controls, etc. , has been becoming one of the mainstream research and development activities (structure & motion) in recent years. These new systems and devices could bring a new technological revolution in modern industries and further, directly or indirectly, impact human life. In the search for and research in innovative technologies, it is proved that piezoelectric materials are very versatile in both sensor and actuator applications. Consequently, piezoelectric technology has been widely applied to a large number of industrial applications and devices, varying from thin-film micro sensors/actuators to large space structures in addition to those relatively conventional applications, e. g. , sensors, actuators, hydrophones, precision manipulators, mobile robots, micro motors, etc. There have been a few books on piezoelectricity published in the past; however, a unified presentation of piezoelectric shells and distributed senSing/control applications is still lacking. This book is intended to fill the gap and to pro~de practising engineers and researchers with an introduction to advanced piezoelectric shell theories and distributed sensor/actuator technologies in structural identification and control. This book represents a collection of the author's recent research and development on piezoelectric shells and related applications to distributed measurement and control of continuaj it reflects six best-paper awards, including [ xviii] • Contents. two ASME Best-Paper Awards in recent years.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
The discovery of piezoelectric phenomena in 1880 led science and technology into a new dimension. It has been over one hundred and twelve years (1880–1992) since the first observation of piezoelectric phenomena by the Curie brothers. Over the years, sophisticated piezoelectricity theories were proposed and refined; new piezoelectric materials were discovered or synthesized (Mason, 1950; Cady, 1964; Mindlin, 1961&1972; Tiersten, 1969; Sesseler, 1981; Dökmeci, 1983; Tzou & Zhong, 1990; etc.). Novel piezoelectric devices were invented and applied to a variety of engineering applications (Mason, 1981; Sessler, 1981; Dökmeci, 1983; Tzou, 1990&1992b; Tzou & Fukuda, 1992). In the recent development of active adaptive structures and micro—electromechanical systems, active piezoelectric and elastic/piezoelectric structures (elastic materials integrated with piezoelectric sensors/actuators and control electronics) and thin—layer piezoelectric devices are very promising in both static and dynamic applications, e.g., aerospace/aircraft structures, robot manipulators, vibration controls and isolations, high—precision devices, micro—sensors/actuators, thin—film micro—electromechanical systems, micro—displacement actuation and control, etc (Tzou & Fukuda, 1991&1992). All these activities have driven a renewed and widely spread interest in piezoelectricity related researches and developments.
H. S. Tzou

Chapter 2. Piezoelectric Shell Vibration Theory

Abstract
Active piezoelectric structures capable of self—adaptation (Tzou & Anderson, 1992) and high—precision operations (Tzou & Fukuda, 1992) have drawn much attention in recent years. In this chapter, generic vibration theories of deep piezoelectric shell continua are derived. The system equations include both mechanical and electric components. The mechanical components are related to conventional elastic vibrations of shells; the electric components are electromechanical coupling effects induced by the piezoelectricity. Eliminating these electromechanical coupling terms from the generic piezoelectric system equations yields a set of conventional vibration equations for elastic shell continua. Note that the electromechanical coupling terms can also be used in sensor and actuator applications applied to distributed identification and controls of shells. (Detailed discussions will be presented in later chapters.) A background introduction and a brief review of the subject area are presented first. Detailed derivations of the piezoelectric shell theory using Hamilton’s principle are presented next. Simplification of the piezoelectric shell vibration theory to the conventional elastic shell vibration theory is also discussed. Applications of the generic theories to commonly occurring geometries, e.g., spherical shells, cylindrical shells, plates, etc., and distributed control of piezoelectric shells are demonstrated in Chapter 3.
H. S. Tzou

Chapter 3. Common Piezoelectric Continua and Active Piezoelectric Structures

Abstract
In this chapter, a simple reduction procedure is developed to apply the generic piezoelectric shell theories to other common piezoelectric continua, such as shells of revolutions, spheres, cylindrical shells, plates, etc (Tzou and Zhong, 1990). Note that the generic piezoelectric thin shell theory is used as the fundamental theory in the later derivations and analyses. Equations of motion of corresponding thin elastic shells can be easily derived by eliminating all electromechanical coupling terms in the piezoelectric shell equations.
H. S. Tzou

Chapter 4. Distributed Sensing and Control of Elastic Shells

Abstract
The inherent natural damping of continua is usually not sufficient enough to effectively and quickly suppress the oscillations of high—performance structural systems, e.g., aerospace structures. Thus, effective vibration control techniques become necessary. Vibration control techniques are generally classified into two major categories: passive and active (Reinhorn & Manolis, 1985). The passive vibration control techniques are based on energy absorption or dissipation principles (Tzou, 1988a), e.g., viscoelastic dampers, dynamic absorbers, shock absorbers, friction dampers, etc. Active vibration controls usually rely on counteracting mechanisms which generate opposing forces or moments to counteract the undesirable oscillations. One of the major advantages of active devices over passive devices is a “self—adaptivity” which offers variable control for various operational environments. However, because of this active actuation capability, external power sources (e.g., electrical, hydraulic, pneumatic, etc.) and a decision—making “brain” (such as a central processing unit) are usually required (Tzou & Gadre, 1988, 1990). In addition, active controls also depend on accurate measurements of current dynamic states. Thus, sensors or transducers are also essential to monitor the structural states in active controls. Both sensors and actuators described are made of distributed piezoelectric layers in this chapter, as well as in the book.
H. S. Tzou

Chapter 5. Multi-Layered Shell Actuators

Abstract
Due to the rapid development of adaptive structures and large flexible systems, “intelligent” or “smart” structures with built in sensors, actuators, and even control electronics are increasingly in demand today (Tzou & Anderson, 1992; Wada, Fanson, & Crawley, 1989). Conventional composite materials have been available for decades, and they are constantly being advanced in many features, such as strength/weight ratios, directional properties, high-temperature tolerance, etc. A step beyond the conventional material improvement is an addition of “intelligence”, i.e., sensors, actuators, control electronics, central processing unit (CPU), etc., to the composites. This chapter presents a theoretical development of a multi-layered thin shell with internal distributed actuators for distributed vibration controls of active shell structures.
H. S. Tzou

Chapter 6. Boundary Control of Beams

Abstract
In this chapter, distributed vibration control of a laminated elastic beam is studied. It is assumed that two thin layers of a mono—axially oriented piezoelectric material, i.e., d31 only and d32 = 0, are respectively bonded on the top and bottom surfaces of the elastic beam. One layer serves as a distributed sensor and the other as a distributed actuator. The effective axis of the piezoelectric layers is aligned with the x—axis to ensure the maximum piezoelectric effects in sensor and actuator applications. It is intended to use the distributed sensor signal as a feedback reference in a closed—loop feedback control system. Two control algorithms, namely a displacement feedback and a velocity feedback are implemented and their control effectiveness evaluated. In the displacement feedback, the distributed sensor signal is amplified and fed back to the distributed piezoelectric actuator. (Note that the sensor signal is proportional to strains which can be ultimately expressed in terms of displacements as presented in Chapter 4. Thus, the conventional “displacement” feedback is used. In general, the dominating vibration component contributes to a higher strain level and consequently to a higher percentage of the total output signal.) In the velocity feedback, this sensor output is differentiated, amplified, and then fed back into the distributed actuator. (Note that the signal used in the velocity feedback is actually a strain/unit-time. Since the strain is ultimately expressed in terms of displacements, the time derivative of the displacement is the velocity.
H. S. Tzou

Chapter 7. Distributed Control of Plates with Segmented Sensors and Actuators

Abstract
Integrating active materials, such as piezoelectrics, shape—memory alloys, electrostrictive materials, magnetostrictive materials, electrorheological fluids, etc., with elastic structures transforms the structures from a completely passive system to an active adaptive system (Tzou, 1991a). With the rapid development of VLSI technologies, adding an “intelligence” to the structure could also become a reality in the near future (Tzou & Fukuda, 1991&1992).
H. S. Tzou

Chapter 8. Convolving Shell Sensors and Actuators Applied to Rings

Abstract
Spillover problems can occur when modal cross couplings introduced by the residual modes come into feedback in a closed—loop distributed control system. Observation spillover is due to the infinite summation of feedback control forces in the closed—loop control equations, and this spillover can introduce unstable dynamic responses in undamped structural systems (Meirovitch & Baruh, 1983). Thus, it is highly desirable that sensors only monitor those modes needed to be controlled such that observation spillover is prevented. In reality, however, sensors not only respond to controlled modes, but also those uncontrolled residual modes. There are several techniques of reducing the observation spillover. Conventional practice is to place sensors, spatially discrete sensors, at modal nodes or nodal lines of the residual modes. The difficulty with this arrangement is that it is very difficult, if not impossible, to avoid all uncontrolled residual modes. Another common approach is to pre—filter the sensor data using a comb filter with phase—locked loops (Gustafson & Speyer, 1976). The phase—locked loop filter reduces the observation spillover in the frequency domain. This technique requires that 1) the controlled modal frequencies are precisely known; 2) there is a reasonable separation from the nearby residual modes; 3) the signal—to—noise ratio is sufficiently high. The other method is to use spatially distributed modal sensors which respond only to a structural mode or a group of modes. In addition, feedback control forces for controlled modes could also appear in the governing equations of other uncontrolled modes resulting from modal interactions among all participating modes — control spillover.
H. S. Tzou

Chapter 9. Sensing and Control of Cylindrical Shells

Abstract
Generic theories for distributed convolving modal sensors and actuators have been proposed in Chapter 8. In this chapter, distributed piezoelectric sensors and actuators designed for structural sensing and control of cylindrical shells are presented. Free vibration analysis of cylindrical shells is presented first and then distributed sensing and control via distributed piezoelectric sensors and actuators. Detailed electromechanics and performances of the sensors and actuators laminated on the cylindrical shells are discussed (Zhong, 1991). Note that there are three cylindrical shells discussed in this chapter: 1) a piezoelectric cylindrical shell, 2) an elastic cylindrical shell, and 3) a laminated cylindrical shell. The differences between the first two cases are: 1) the electric and electromechanical coupling terms and 2) a charge equation of electrostatics. The laminated cylindrical shell is made of an elastic shell whose inner and outer surfaces are laminated with distributed piezoelectric layers. These piezoelectric layers are used as a distributed sensor and an actuator respectively.
H. S. Tzou

Chapter 10. Finite Element Formulation and Analyses

Abstract
The rapid development of high—speed computers has facilitated the use of computational techniques in a variety of engineering applications. Today, the finite element method is one of the most popular and powerful techniques in modern engineering design and analysis of complicated structures and multi—field problems. In recent years, however, researches on active piezoelectric structures have focused primarily on experimental and theoretical studies; there has been little general—purpose piezoelectric finite element development (Tzou & Tseng, 1988a&b; Allik & Hughes, 1979; Nailon, et al., 1983).
H. S. Tzou

Backmatter

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