Vibrations of Linear Piezostructures. Andrew J. Kurdila

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       Library of Congress Cataloging-in-Publication Data

      Names: Kurdila, Andrew, author. | Tarazaga, Pablo (Pablo A.), author.

      Title: Vibrations of linear piezostructures / Andrew J. Kurdila and Pablo A. Tarazaga.

      Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2021. | Series: Wiley-ASME Press series | Includes bibliographical references and index.

      Identifiers: LCCN 2020027699 (print) | LCCN 2020027700 (ebook) | ISBN 9781119393405 (cloth) | ISBN 9781119393504 (adobe pdf) | ISBN 9781119393528 (epub) | ISBN 9781119393382 (obook)

      Subjects: LCSH: Piezoelectricity. | Vibration.

      Classification: LCC QC595 .K78 2021 (print) | LCC QC595 (ebook) | DDC 537/.2446--dc23

      LC record available at https://lccn.loc.gov/2020027699

      LC ebook record available at https://lccn.loc.gov/2020027700

      Cover Design: Wiley

      Cover Image: Pablo A. Tarazaga

Foreword

      The rise of piezoelectric materials as sensors and actuators in engineering systems got started around 1980 and began to make an impact in the world of vibrations about five years after that. Subsequently, it started to explode into the 90s with topics such shunt damping, active control, structural health monitoring and energy harvesting. As a result, the need to document the fundamentals and intricacies of modeling piezoelectric materials in the context of vibrations in book form will well serve a variation of communities. The presentation here puts the topic on a firm mathematical footing.

      The authors are uniquely qualified to provide a sophisticated analytical framework with an eye for applications. Professor Kurdila has nearly four decades of experience in modeling of multi‐physics systems. He authored two other books, one on structural dynamics, and several research monographs. Professor Tarazaga is an experienced creator of piezoelectric solutions to vibration and control problems. Both are well published in their respective research areas of research. Their combined expertise in researching vibratory systems integrated with piezoelectric materials enables this complete and detailed book on the topic. This allows for a formal theoretical background which will enable future research.

      Daniel J. Inman

      Ann Arbor, Michigan

Preface

      The goal of this book is to provide a self‐contained, comprehensive, and introductory account of the modern theory of vibrations of linearly piezoelectric structural systems. While the piezoelectric effect was first investigated by the Curies in the

, and systematically investigated in the field of acoustics and the development of sonar during the First World War, it is only much more recently that we have seen the widespread interest in mechatronic systems that feature piezoelectric sensors and actuators. Many of the early, now classical, texts present piezoelectricity from the viewpoint of a material scientist such as in [22] or [53]. Others are difficult, if not impossible, to obtain since they are out of print. Older editions of the excellent text [20] are currently selling for prices in excess of $600 on sites such as Amazon.com. Moreover, it is also quite difficult to find treatments of piezoelectricity that systematically cover all the relevant background material from first principles in continuum mechanics, continuum electrodynamics, or variational calculus that are necessary for a comprehensive introduction to vibrations of piezoelectric structures. The authors know of no text that assimilates all this requisite supporting material into one source. One text may give an excellent overview of piezoelectric constitutive laws, but neglect to discuss variational methods. Another may cover variational methods for piezoelectric systems, but fail to review the first principles of electrodynamics, and so forth. A large, substantive literature on various aspects of piezoelectricity has evolved over the past few years in archival journal articles, but much of this material has never been systematically represented in a single text.

This book has evolved from the course notes that the authors have generated while offering courses in active materials, smart systems, and piezoelectric materials over the past decade at various research universities. Most recently, the authors have taught active materials and smart structures courses that feature piezoelectricity at Virginia Tech to a diverse collection of first year graduate students. So much time was dedicated to the particular systems that include piezoelectric components that this textbook emerged. The backgrounds of the students in our classes have varied dramatically. Many students have not had a graduate class in vibrations, continuum mechanics, advanced strength of materials, nor electrodynamics. For this reason, the notes that evolved into this book make every effort to be self‐contained. Admittedly, this text covers in one chapter what other courses may cover over one or two semesters of dedicated study. As an example, Chapter 3 reviews the fundamentals of continuum mechanics for this text, a topic that is covered in other graduate classes at an introductory level during a full semester. So, while the presentation attempts to be comprehensive, the pace is sometimes brisk.

      While preparing this text, we have tried to structure the material so that it is presented at the senior undergraduate or first year graduate student level. It is intended that this text provide the student with a good introduction to the topic, one that will serve them well when they seek to pursue more advanced topics in other texts or in their research. For example, this text can serve as a introduction to the fundamentals of modeling piezoelectric systems, and it can prepare the student specializing in energy harvesting when they consult a more advanced text such as [21].

      This text begins in Chapter 2 with a review of the essential mathematical tools that are used frequently throughout the book. Topics covered include frames, coordinate systems, bases, vectors, tensors, introductory crystallography, and symmetry. Chapter 3 then gives a fundamental summary of topics from continuum mechanics. The stress vector and tensor is defined, Cauchy's Principle and the equilibrium equations are derived. The strain tensor is defined, and an introduction to constitutive laws for linearly elastic materials is also covered in this chapter. Chapter 4 provides the student the required introduction to continuum