Plates and Shells for Smart Structures E-Book

Erasmo Carrera

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 331

Veröffentlichungsjahr: 2011

Beschreibung

Smart structures that contain embedded piezoelectric patches are loaded by both mechanical and electrical fields. Traditional plate and shell theories were developed to analyze structures subject to mechanical loads. However, these often fail when tasked with the evaluation of both electrical and mechanical fields and loads. In recent years more advanced models have been developed that overcome these limitations.

Plates and Shells for Smart Structures offers a complete guide and reference to smart structures under both mechanical and electrical loads, starting with the basic principles and working right up to the most advanced models. It provides an overview of classical plate and shell theories for piezoelectric elasticity and demonstrates their limitations in static and dynamic analysis with a number of example problems. This book also provides both analytical and finite element solutions, thus enabling the reader to compare strong and weak solutions to the problems.

Key features:

• compares a large variety of classical and modern approaches to plates and shells, such as Kirchhoff-Love , Reissner-Mindlin assumptions   and higher order, layer-wise and mixed theories
• introduces theories able to consider electromechanical couplings as well as those that provide appropriate interface continuity conditions for both electrical and mechanical variables
• considers both static and dynamic analysis
• accompanied by a companion website hosting dedicated software MUL2 that is used to obtain the numerical solutions in the book, allowing the reader to reproduce the examples given as well as solve problems of their own

The models currently used have a wide range of applications in civil, automotive, marine and aerospace engineering. Researchers of smart structures, and structural analysts in industry, will find all they need to know in this concise reference. Graduate and postgraduate students of mechanical, civil and aerospace engineering can also use this book in their studies.

www.mul2.com

Leseprobe

Contents

Cover

Title Page

Copyright

About the Authors

Preface

1: Introduction

1.1 Direct and inverse piezoelectric effects

1.2 Some known applications of smart structures

References

2: Basics of piezoelectricity and related principles

2.1 Piezoelectric materials

2.2 Constitutive equations for piezoelectric problems

2.3 Geometrical relations for piezoelectric problems

2.4 Principle of virtual displacements

2.5 Reissner mixed variational theorem

References

3: Classical plate/shell theories

3.1 Plate/shell theories

3.2 Complicating effects of layered structures

3.3 Classical theories

3.4 Classical plate theories extended to smart structures

3.5 Classical shell theories extended to smart structures

References

4: Finite element applications

4.1 Preliminaries

4.2 Finite element discretization

4.3 FSDT finite element plate theory extended to smart structures

References

5: Numerical evaluation of classical theories and their limitations

5.1 Static analysis of piezoelectric plates

5.2 Static analysis of piezoelectric shells

5.3 Vibration analysis of piezoelectric plates

5.4 Vibration analysis of piezoelectric shells

References

6: Refined and advanced theories for plates

6.1 Unified formulation: refined models

6.2 Unified formulation: advanced mixed models

6.3 PVD(u, Φ) for the electromechanical plate case

6.4 RMVT(u, Φ, σn) for the electromechanical plate case

6.5 RMVT(u, Φ, ) for the electromechanical plate case

6.6 RMVT(u, Φ, σn, ) for the electromechanical plate case

6.7 Assembly procedure for fundamental nuclei

6.8 Acronyms for refined and advanced models

6.9 Pure mechanical problems as particular cases, PVD(u) and RMVT(u, σn)

6.10 Classical plate theories as particular cases of unified formulation

References

7: Refined and advanced theories for shells

7.1 Unified formulation: refined models

7.2 Unified formulation: advanced mixed models

7.3 PVD(u, Φ) for the electromechanical shell case

7.4 RMVT(u, Φ, σn) for the electromechanical shell case

7.5 RMVT(u, Φ, ) for the electromechanical shell case

7.6 RMVT(u, Φ, σn, ) for the electromechanical shell case

7.7 Assembly procedure for fundamental nuclei

7.8 Acronyms for refined and advanced models

7.9 Pure mechanical problems as particular cases, PVD(u) and RMVT(u, σn)

7.10 Classical shell theories as particular cases of unified formulation

7.11 Geometry of shells

7.12 Plate models as particular cases of shell models

References

8: Refined and advanced finite elements for plates

8.1 Unified formulation: refined models

8.2 Unified formulation: advanced mixed models

8.3 PVD(u, Φ) for the electromechanical plate case

8.4 RMVT(u, Φ, σn) for the electromechanical plate case

8.5 RMVT(u, Φ, ) for the electromechanical plate case

8.6 RMVT(u, Φ, σn, ) for the electromechanical plate case

8.7 FE assembly procedure and concluding remarks

References

9: Numerical evaluation and assessment of classical and advanced theories using MUL2 software

9.1 The MUL2 software for plates and shells: analytical closed-form solutions

9.2 The MUL2 software for plates: FE solutions

9.3 Analytical closed-form solution for the electromechanical analysis of plates

9.4 Analytical closed-form solution for the electromechanical analysis of shells

9.5 FE solution for the electromechanical analysis of beams

9.6 FE solution for the electromechanical analysis of plates

References

Index

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Library of Congress Cataloguing-in-Publication Data

Carrera, Erasmo. Plates and shells for smart structures : classical and advanced theories for modeling and analysis / Erasmo Carrera, Salvatore Brischetto, Pietro Nali. -- 1st ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-97120-8 (hardback) 1. Shells (Engineering) 2. Plates (Engineering) 3. Smart structures. I. Brischetto, Salvatore. II. Nali, Pietro. III. Title. TA660.S5C276 2011 624.1′776--dc23 2011019535

A catalogue record for this book is available from the British Library.

Print ISBN: 9780470971208

ePDF ISBN: 9781119950011

oBook ISBN: 9781119950004

ePub ISBN: 9781119951124

Mobi ISBN: 9781119951131

About the Authors

Erasmo Carrera

After earning two degrees (Aeronautics, 1986, and Aerospace Engineering, 1988) at the Politecnico di Torino, Erasmo Carrera received his PhD in Aerospace Engineering in 1991, jointly at the Politecnico di Milano, Politecnico di Torino, and Università di Pisa. He began working as a Researcher in the Department of Aeronautics and Space Engineering at the Politecnico di Torino in 1992 where he held courses on Missiles and Aerospace Structures Design, Plates and Shells, and the Finite Element Method, and where he has been Professor of Aerospace Structures and Aeroelasticity since 2000. He has visited the Institut für Statik und Dynamik, Universität Stuttgart twice, the first time as a PhD student (6 months in 1991) and then as Visiting Scientist under a GKKS Grant (18 months from 1995). In the summer of 1996 he was Visiting Professor at the ESM Department of Virginia Tech. He was also Visiting Professor for two months at SUPMECA, Paris, in 2004, and at CRP H. Tudor, G.D. Luxembourg, in 2009. His main research topics are: composite materials, FEM, plates and shells, postbuckling and stability, smart structures, thermal stress, aeroelasticity, multibody dynamics, non-classical lifting systems and multifield problems. Professor Carrera has made significant contributions to these topics. In particular, he proposed the Carrera Unified Formulation to develop hierarchical beam/plate/shell theories and finite elements for multilayered structure analysis as well as the generalization of classical and advanced variational methods for multifield problems. He has been responsible for various research contracts with the EU and national and international agencies/industries. Presently, he is Full Professor and Deputy Director of his department. He is the author of more than 300 articles, many of which have been published in international journals. He serves as a referee for many journals, and as contributing editor for Mechanics of Advanced Materials and Structures, Composite Structures and Journal of Thermal Stresses. He has also served on the Editorial Boards of many international conferences.

Salvatore Brischetto

After earning his degree in Aerospace Engineering at the Politecnico di Torino in 2005, Salvatore Brischetto received his PhD in Aerospace Engineering (Politecnico di Torino) and in Mechanics (Université Paris Ouest–Nanterre La Défense) in 2009. He won the excellence prize for PhD students at the Politecnico di Torino in 2008. Dr Brischetto worked as a Research Assistant in the Department of Aeronautics and Space Engineering at the Politecnico di Torino from 2006 to 2010, and has been Assistant Professor in the same department since 2010. His main research topics are: smart structures, composite materials, multifield problems, functionally graded materials, thermal stress analysis, carbon nanotubes, inflatable structures, and plate and shell finite elements. He is the author of more than 50 articles on these topics, more than half of which have been published in international journals. He serves as a reviewer for some international journals, such as Composite Structures, Journal of Mechanics of Materials and Structures, Applied Mathematical Modeling, Journal of Applied Mechanics, Journal of Composite Materials, etc. He has also been Guest Editor for Mechanics of Advanced Materials and Structures for the Special Issues entitled “Modeling and analysis of functionally graded beams, plates and shells, Parts I and II.” He has been Teaching Assistant at the Politecnico di Torino for courses on computational aeroelasticity, structures for aerospace vehicles and nonlinear analysis of aerospace structures since 2007.

Pietro Nali

After earning his degree in Aerospace Engineering in 2005 at the Politecnico di Torino, Pietro Nali held a traineeship at the European Space Agency/ESTEC, Structures and Thermal Division, from August 2005 to February 2006. He was the candidate from the Politecnico di Torino for an ESA NPI (Networking/ Partnering Initiative) position in 2006. He received his PhD in Aerospace Engineering (Politecnico di Torino) and in Mechanics (Université Paris Ouest–Nanterre La Défense) within the framework of the NPI, in 2010, for the topic “Modeling and validation of multilayered structures for spacecraft, including multifield interactions.” Since 2010, Dr Nali has worked as a Research Assistant in the Department of Aeronautics and Space Engineering at the Politecnico di Torino. His main research topics are: finite elements, multilayered plate modeling, smart structures, composite materials, failure criteria, multifield problems, thermal stress analysis, and structure nonlinearities.

Preface

Smart structures involve interactions between mechanical and electric fields. Classical models for beams, plates, and shells were originally developed to compute stress fields due to the application of mechanical loadings. These classical models have demonstrated certain difficulties and limitations in the analysis of smart structures. Electrical loadings are in fact “field loadings” which require the use of advanced structural models. Smart structures, in most applications, are layered structures with piezoelectric patches/layers. Layered structures have, by definition, several “interfaces.” Interfaces lead to discontinuous distributions along the thickness of both the electrical and mechanical properties. This book presents a detailed analysis of classical and advanced structural models that are able to deal with mechanical and electric field loadings. Assumptions are made on displacements, transverse stresses, electric potential, and transverse electric displacements. Extensions of the principle of virtual displacements (PVD) and of the Reissner mixed variational theorem (RMVT) are used to derive governing equations and finite element matrices of laminated plate/shell structures embedding piezoelectric layers. Assumptions on the unknown variables are introduced through the application of the Carrera Unified Formulation, where the accuracy of the models can be enriched by preserving the form of governing equations and finite element matrices, which are written in terms of a few fundamental nuclei. A large variety of plate/shell models are built and compared. Classical theories, based on Kirchhoff–Love and Reissner–Mindlin assumptions, are obtained as particular cases. The classical and advanced structural models discussed in this book have been coded using the academic in-house software MUL2 (MULtifield problems for MULtilayered structures). MUL2 has been used in most of the quoted numerical calculations. An updated version of these codes is available to buyers of this book at http://www.mul2.com.

www.wiley.com/go/carrera

1

Introduction

In many national and international declarations, it has been stated that developments in advanced structures, in the automotive and shipbuilding industries, as well as in aeronautical and space sciences, are subordinate to the development of so-called smart structures.

The definition of smart structures has been extensively discussed since the late 1970s. A workshop was organized by the US Army Research Office in 1988 in order to propose a definition of smart systems/structures to be adopted by the scientific community (Ahmad 1988):

A system or material which has built-in or intrinsic sensor(s), actuator(s) and control mechanism(s) whereby it is capable of sensing a stimulus, responding to it in a predeterminated manner and extent, in a short/appropriate time, and reverting to its original state as soon as the stimulus is removed.

According to design practices, smart structures are systems that are capable of sensing and reacting to their environment, through the integration of various elements, such as sensors and actuators. Smart structures can allow their shape to be varied to very high precision and without using classical mechanical actuators, alleviate vibrations and acoustic noise, and even monitor their own structural health.

Piezoelectric, piezomagnetic, electrostrictive, and magnetostrictive materials are of interest when designing smart structures. Shape memory alloys, electrorheological fluids, and fiber optics should also be mentioned. This book deals with smart structures, taking advantage of piezoelectric effects.

Nowadays, it is difficult to foresee whether smart structures will be employed to any great extent in the future. However, interest in a better understanding of the topic appears essential and could lead to many other uses related to other extensive domains of application.

1.1 Direct and inverse piezoelectric effects

Piezoelectricity was discovered by Jacques and Pierre Curie in 1880, when they realized that several kinds of crystals were able to generate positive or negative electric charges when subjected to mechanical pressure (Curie and Curie 1880, 1881). When dealing with piezoelectric materials, a charge is generated when molecular electrical dipoles are caused by a mechanical loading: that is, the direct effect (sensor configuration). Conversely, when an electric charge is applied, a slight change occurs in the shape of the structure: that is, the inverse effect (actuator configuration). It has been demonstrated that piezoelectric materials can be used at the same time as actuators and sensors, obtaining the so-called self-sensing piezoelectric actuator (Dosh et al. 1992).

Piezoelectricity is a feature of some natural crystals (such as quartz and tourmaline) or synthetic crystals (lithium sulfate), and several kinds of polymers and polarized ceramics. The most common piezoelectric materials are the piezoceramic barium titanate (BaTiO3) and piezo lead zirconate titanate (PZT). The crystal lattice of piezoelectric materials is of the face-centered cubic (FCC) kind. Metallic atoms are located at the vertex of the cube, while oxygen atoms remain at the center of the cube’s faces. A heavier atom is located at the center of the cube and it can shift slightly to positions with less energy, with a consequent deformation of the crystal lattice (metastable structure). If an electric field is applied to the structure, the central atom can exceed the potential energy threshold and move to a lower energy configuration. This is followed by a rupture of symmetry and the creation of an electric dipole (Figure 1.1). The previous phenomenon is possible only below the so-called Curie temperature. Above this temperature, the piezoelectric effect disappears due to high thermal agitation. Polarized piezoceramics are obtained by heating them above their Curie temperature and subjecting the material to an intense electric field during thermal cooling. In so doing, all the dipoles become oriented in the same direction and the material obtains a stable polarization. Moreover, apart from a residual polarization, the crystal lattice of the polarized piezoceramic will also undergo a residual deformation. After the polarization process, a very small electric potential will be sufficient to obtain a temporary deformation and vice versa.

Figure 1.1 Piezoceramic cell before (left) and after (right) polarization.

Even if the electro mechanical coupling is a nonlinear phenomenon, piezoelectric problems are usually studied through linear analysis. This leads to the adoption of assumptions, which will be discussed in Chapter 2. Additional details on this topic can be found in the works by Cady (1964), Tiersten (1969), and Ikeda (1996).

1.2 Some known applications of smart structures

Smart structures have been used in sensing, actuating, diagnosing, and assessing the health of structures, depending on the external stimuli. Sensors and actuators should be integrated into the complete structures and this leads to unusual design solutions, compared to traditional structural design solutions (Srinivasan and McFarland 2001). In the most advanced design concepts, smart structures could have the ability to save and analyze information in order to perform a learning process.

Nowadays, smart structures are applied in many different domains, but they all share the common feature of having a highly cross-disciplinary design. Among other applications, the following current/potential ones can be mentioned.

Structural health monitoring The strain field of some critical locations of a generic structural system can be measured using embedded sensors in order to identify possible damage and retain structural safety and reliability. Damage is intended here as a variation of the material and/or geometric properties, which could affect the performances of the systems. Self-diagnostic ability plays a crucial role in the aeronautical and space industry, where sensing the strain field of some relevant structural subcomponents helps in the conduction of an appropriate maintenance program and in avoiding crack propagation. This topic appears of particular interest for composite materials, whose failure prediction is a challenging task. Composites are being progressively employed more and more in aerospace engineering in order to replace metallic structures. As a consequence, structural health monitoring will become a very important task in the near future. In principle, crack propagation could be restrained by producing compressive stresses around the failure through a proper network of embedded actuators (Rogers, 1990). Rogers (1990) also mentioned the possibility of using skin-like tactile piezoelectric sensors to sense temperatures and pressures. Structural health monitoring is also applied extensively in civil engineering. The most well-known examples refer to the remote monitoring of bridge deflections, mode shapes, and the corresponding frequencies (Deix et al. 2009; Spuler et al. 2009). The scheme of the Saint Anthony Falls Bridge in Figure 1.2 represents an example of a smart system with embedded devices that offers optimal diagnostics (Foster 2009). Monitoring is usually performed by analyzing the dynamic response of a system through an array of properly located sensors. Periodic observations and comparisons to previous measurements and numerical simulations can indicate some local damage or structural/material degradation resulting from the operational environment.

Figure 1.2 Smart system scheme of the Saint Anthony Falls Bridge for structural health monitoring.

Vibration control Due to their high strain sensitivity (Sirohi and Chopra 2000), piezoelectric sensors and actuators are easily employed for vibration damping/attenuation/suppression (Inman et al. 2001). Piezoceramics are used to reduce noise and improve the comfort of vehicles, such as cars, trucks, and helicopters, and to improve the performances of machine tools. The same technique is often employed in spacecraft carrying equipment in a pure operational dynamic environment. Active vibration control is usually applied in engineering practice in order to suppress dangerous vibrations over a certain range of frequencies, as in the case of helicopter blades (Chopra 2000). Piezoelectric materials are also effective in passive damping: a part of the mechanical energy introduced into the structural system is converted into electrical energy, according to the piezoelectric effect. Piezoelectric passive damping devices are commonly embedded in high-performance sports devices, such as tennis rackets, baseball bats, and skis (Gaudenzi 2009).

Shape morphing Among the possible shape morphing industrial applications of structural components, focusing on the aeronautics field, it is worth mentioning the advantages of a wing with variable shape. Commercial aircraft have to respect increasing efficiency requirements and reduce emissions. One possible solution is to propose a variable shape wing that is able to optimize performances in all phases of the mission. The means that can be employed to vary the shape of the wing are quite challenging and can vary in complexity, depending on which properties have to be modified: sweep angle, profile, aspect ratio, etc. Swept wings (as a solution to reduce wave drag) were first used on jet fighter aircraft. Variable shape wings, in a broad sense, could play a significant role in future aircraft designs. The elementary wing shape changes for take-off/cruise/landing are currently obtained by means of rigid body motions of movable parts, e.g., flaps, slats, ailerons, and spoilers. It is understood that a smart flexible wing, without secondary parts, that would be able to perform proper shape changes, would lead to a remarkable reduction in drag, weight, and overall system complexity; see Figure 1.3 for an example of a hingeless flap that can be obtained from shape morphing.

Figure 1.3 Wings with conventional flaps (left) and with smart flexible flaps (right).

Active optics Active optics, which are usually employed in large reflector telescopes and can be considered as a particular case of shape morphing, allow the shape of mirrors to be monitored and readjusted during operation. In this way, it is possible to avoid effects due to gravity or wind (in the case of an Earth-based telescope) or deformations due to thermo mechanical coupling or structural imperfections (in the case of space telescopes). The use of accurate actuators, together with an algorithm that is able to quantify the quality of images, allow a precision to be obtained that goes well beyond the possibilities of conventional reflector telescopes. Active optics are currently employed in 10 m class telescopes and are also going to be applied in the next generation of 40 m telescopes (Preumont et al. 2009).

Microelectromechanical systems (MEMS) MEMS consist of extremely small mechanical devices driven by electricity. A device’s dimensions vary from 20 m to 1 mm. MEMS devices can be used as multiple microsensors and microactuators (Varadan and Varadan 2002). MEMS are particularly promising in the medical field, where they can be employed as blood sugar sensors, insulin delivery pumps, micromotor capsules that unclog arteries, or filters that expand after insertion into a blood vessel in order to trap blood clots (Srinivasan and McFarland 2001).

Many potential benefits can be obtained due to the extensive use of smart structures in industrial applications. Reducing maintenance costs, in the case of self-diagnostic structural health monitoring, should be mentioned. In fact, maintenance time is a crucial point for airlines, which, according to the low-cost business philosophy, has greatly reduced profit margins. Another benefit consists of the possibility of producing new components, according to new design concepts, like shape morphing and the integration of MEMS in structures. It should also be emphasized that MEMS are currently enlarging medical perspectives, and opening up new scenarios for the future of health care programs.

Aim of this book This book aims to illustrate the classical techniques and some advanced models that are able to describe mechanical and electrical variables in plate/shell structures that have piezoelectric layers embedded in the lamination stacking sequence. Two-dimensional axiomatic models are considered through analytical and finite element approaches. Classical models (e.g., Kirchhoff, Mindlin, and equivalent single-layer kinematic descriptions) are compared to advanced theories (mixed, layer wise, and higher order descriptions) through several numerical examples. Most of the presented theories are derived on the basis of the Carrera Unified Formulation, which probably is one of the most modern and advanced tools for dealing with the theory of structures.

References

Ahmad I 1988 Smart structures and materials. In Proceedings of US Army Research Office Workshop on Smart Materials, Structures and Mathemetacal Issues.

Cady WG 1964 Piezoelectricity. Dover.

Chopra I 2000 Status of application of smart structures technology to rotorcraft systems. J. Am. Helicopter Soc.45, 228–252.

Curie J and Curie P 1880 Développement par compression de l’électricitè polaire dans les cristaux hémièdres a faces inclinées. C. R. Acad. Sci. Paris91, 294–295.

Curie J and Curie P 1881 Contractions et dilatations produites par des tensions électriques dans des cristaux hémièdres a faces inclinées. C. R. Acad. Sci. Paris93, 1137–1140.

Deix S, Ralbovsky M, Stuetz R, and Wittmann SM 2009 Structural health monitoring using wireless sensor networks. In Proceedings of the IV ECCOMAS Thematic Conference on Smart Structures and Materials.

Dosh JJ, Inman DJ, and Garcia E 1992 Self-sensing piezoelectric actuator for collocated control. J. Intell. Mater. Syst. Struct.3, 166–185.

Foster D 2009 The bridge to smart technology. In Bloomberg Businessweek.

Gaudenzi P 2009 Smart Structures: Physical Behaviour, Mathematical Modelling and Applications. John Wiley & Sons, Ltd, UK.

Ikeda T 1996 Fundamentals of Piezoelectricity. Oxford University Press.

Inman DJ, Ahmadihan, M and Claus RO 2001 Simultaneous active damping and health monitoring of aircraft panels. J. Intell. Mater. Syst. Struct.12, 775–783.

Preumont A, Bastaits R, and Rodrigues G 2009 Active optics for large segmented mirrors: scale effects. In Proceedings of the IV ECCOMAS Thematic Conference on Smart Structures and Materials.

Rogers CA 1990 Intelligent material systems and structures. In Proceedings of US Japan Workshop on Smart/Intelligent Materials and Systems.

Sirohi J and Chopra I 2000 Fundamental understanding of piezoelectric strain sensors. J. Intell. Mater. Syst. Struct.11, 246–257.

Spuler T, Moor G, and Berger R 2009 Modern remote structural health monitoring: an overview of available systems today. In Proceedings of the IV ECCOMAS Thematic Conference on Smart Structures and Materials.

Srinivasan AV and McFarland MD 2001 Smart Structures: Analysis and Design. Cambridge University Press.

Tiersten HF 1969 Linear Piezoelectric Plate Vibrations. Plenum Press.

Varadan VK and Varadan VV 2002 Microsensors, microelectromechanical systems (MEMS) and electronics for smart structures and systems. Smart Mater. Struct.9, 953–972.

2

Basics of piezoelectricity and related principles

The phenomenon of piezoelectricity is described by referring to the most common piezoelectric materials. Fundamental piezoelectricity equations are discussed, the meaning of the coupling coefficients is dealt with in detail, and some available data concerning electromechanical properties are given. The physical and variational principles of piezoelectricity are introduced. First, the principle of virtual displacements is extended to the electromechanical case by simply adding the internal electrical work. Then, three extensions of the Reissner mixed variational theorem, which permits one to consider a priori some transverse mechanical and electrical variables, are briefly discussed. A clear definition of the field variables is given. The constitutive equations of piezoelectricity are explained in detail for the different variational statements that are proposed.

2.1 Piezoelectric materials

The phenomenon of piezoelectricity is a particular feature of certain classes of crystalline materials. The piezoelectric effect is due to a linear energy conversion between the mechanical and electric fields. The linear conversion between the two fields is in both directions, and it thus defines a direct or converse piezoelectric effect. The generates an electric polarization by applying mechanical stresses. The instead induces mechanical stresses or strains by applying an electric field. These two effects represent the coupling between the mechanical and electric fields. The first applications were in the field of submarine detection during World War I. Interest increased after the introduction of PZT (Lead Zirconate Titanate) at the end of the first half of the twentieth century. These ceramic materials offered much higher performances and have thus broadened the possible field of applications. These applications, however, were still limited to sound and ultrasound devices. A description of the early piezoelectric materials can be found in Cady (1964). Kawai (1979), in the late 1970s, discovered another class of piezoelectric materials, the so-called (PVDF), a semi-crystalline polymer with high sensor capability. In recent years, piezoelectricity has been the subject of renewed interest, as inactive intelligent structures with self-monitoring and self-adaptive capabilities. Interesting reviews on these topics can be found in Chopra (2002), Tani (1998), and Rao and Sunar (1994).