Jiashi Yang - Böcker

This book is based on lecture notes for a graduate course that has been offered at University of Nebraska-Lincoln on and off since 1998. The course is intended to provide graduate students with the basic aspects of the continuum modeling of electroelastic interactions in solids. A concise treatment of linear, nonlinear, static and dynamic theories and problems is presented. The emphasis is on formulation and understanding of problems useful in device applications rather than solution techniques of mathematical problems. The mathematics used in the book is minimal. The book is suitable for a one-semester graduate course on electroelasticity. It can also be used as a reference for researchers. I would like to take this opportunity to thank UNL for a Maude Hammond Fling Faculty Research Fellowship in 2003 for the preparation of the first draft of this book. I also wish to thank Ms. Deborah Derrick of the College of Engineering and Technology at UNL for editing assistance with the book, and Professor David Y. Gao of Virginia Polytechnic Institute and State University for recommending this book to Kluwer for publication in the series of Advances in Mechanics and Mathematics. JSY Lincoln, Nebraska 2004 Preface Electroelastic materials exhibit electromechanical coupling. They experience mechanical deformations when placed in an electric field, and become electrically polarized under mechanical loads. Strictly speaking, piezoelectricity refers to linear electromechanical couplings only.

Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. The book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances and new applications in piezoelectricity.

Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. The book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances and new applications in piezoelectricity.

This textbook introduces theoretical piezoelectricity. The second edition updates a classical, seminal reference on a fundamental topic that is addressed in every materials science curriculum. It presents a concise treatment of the basic theoretical aspects of continuum modeling of electroelastic interactions in solids. The general nonlinear theory for large deformations and strong fields is established and specialized to the linear theory for small deformations and weak fields, i.e., the theory of piezoelectricity. Relatively simple and useful solutions of many static and dynamic problems of piezoelectricity that are useful in device applications are given. Emphasis is on the formulation of solutions to problems rather than advanced mathematical solution techniques. This book includes many examples to assist and enhance students’ understanding of piezoelectricity and piezoelastics.

This book presents the mechanics of piezoelectric semiconductor structures where the main electromechanical coupling of interest is the interaction between mechanical fields and semiconduction.

This book presents the mechanics of piezoelectric semiconductor structures where the main electromechanical coupling of interest is the interaction between mechanical fields and semiconduction.

Five appendices appear at the end, which include basic equations of elasticity in cylindrical, polar, and spherical coordinates, as well as a collection of vector identities that appear throughout the book.A Concise Course in Elasticity is an ideal textbook for a one-semester graduate course on elasticity.

As a continuation of the author's previous book An Introduction to the Theory of Piezoelectricity (Springer, New York, 2005) on the three-dimensional theory of piezoelectricity, this book covers one- and two-dimensional theories of piezoelectric structures including rods, beams, plates and shells. In addition to the so-called low-frequency motions of extension and bending, high-frequency motions of thickness shear and thickness stretch are also considered for certain applications unique in resonant piezoelectric devices. Both single-layer and multi-layer structures are treated. Nonlinear effects due to large deflection or large shear deformation are also discussed. The emphasis in on the development of structural theories with various levels of sophistication for different applications in piezoelectric devices.The book is heavily influenced by R D Mindlin's early contributions to this field. It is destined to be one of the most systematic and comprehensive books on piezoelectric structures. This second edition is a major reorganization of the first edition with multiple additions as well as deletion of chapters and sections.

Conventional books on the mechanics of materials treat elastic deformations of solids through one-dimensional models for the extension of rods, torsion of shafts and bending of beams. In functional materials, mechanical, thermal, electric and magnetic fields interact among themselves, and therefore, need a more comprehensive model.This book presents a systematic treatment of the three-dimensional theories for these coupled phenomena and the corresponding one-dimensional models for extension, torsion and bending. This book adopts a mixed approach by devoting the first half of the book to the development of the three-dimensional theories of elastic, thermal, electric and magnetic fields as well as their interactions in dielectrics, conductors and semiconductors. The remainder of the book presents the one-dimensional models for extension, torsion and bending systematically.Related Link(s)

Theory of Electromagnetoelasticity presents a systematic and unique treatment of elastic, electric and magnetic interactions in solids including various thermal and dissipative effects such as viscoelasticity and electrical conduction. In this book, a general and nonlinear continuum theory is constructed. The fundamental building blocks of the theory — the electromagnetic body force, couple and power — are calculated from a multi-continuum model consisting of a lattice continuum for elastic deformation, a bound charge continuum for electric polarization, a circulating current continuum for magnetization, and a free charge fluid for electrical conduction. The multi-continuum model is simpler than the common charged particle model and reveals the underlying physics from a unique angle. The complete set of Maxwell's equations for the electromagnetic fields is included without the widely used quasistatic approximations of the electric and/or magnetic fields. The theory established can be used to describe different kinds of interactions between acoustic and optical fields or waves. Some linear problems are analyzed as examples to show some of the simplest elastic and electromagnetic couplings.

A continuation of the author's previous book “An Introduction to the Theory of Piezoelectricity” (Springer, New York, 2005) on the three-dimensional theory of piezoelectricity, this volume covers lower dimensional theories for various piezoelectric structures and device applications. The development of two-, one- and zero-dimensional theories for high frequency vibrations of piezoelectric plates, shells, beams, rings curved bars and parallelepipeds is systematically presented. In addition to linear piezoelectricity, certain nonlinear effects are also considered and examples for device applications are provided.The material emphasizes dynamic theories and high frequency motions as well as device applications as there are relatively few books on piezoelectric structures, especially for high frequency theories. The volume is destined to be one of the most systematic and comprehensive books on piezoelectric structures.

This is the most systematic, comprehensive and up-to-date book on the theoretical analysis of piezoelectric devices. It is a natural continuation of the author's two previous books: “An Introduction to the Theory of Piezoelectricity” (Springer, 2005) and “The Mechanics of Piezoelectric Structures” (World Scientific, 2006). Based on the linear, nonlinear, three-dimensional and lower-dimensional structural theories of electromechanical materials, theoretical results are presented for devices such as piezoelectric resonators, acoustic wave sensors, and piezoelectric transducers. The book reflects the contribution to the field from Mindlin's school of applied mechanics researchers since the 1950s.

This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.

This book focuses on dynamic antiplane problems of piezoelectric ceramics. It presents relatively simple theoretical solutions to many such problems, and attempts to use these solutions to demonstrate the operation and design of several acoustic wave devices. Some of the solutions are able to show the underlying physics clearly without the need for numerical computation. The problems treated include the propagation of plate waves, surface waves, interface waves, Love waves, gap waves, and vibrations of finite bodies of various shapes with applications in resonators, mass sensors, fluid sensors, interface sensors, phononic crystals, piezoelectric generators or power harvesters, piezoelectric transformers, power or signal transmission through an elastic wall, and acoustic wave excitation and detection for nondestructive evaluation.

The first contemporary text specializing on the dynamic problems of piezoelectric crystal plates for resonant acoustic wave devices (such as resonators, filters, and sensors) since H F Tiersten's publication in 1969. This book provides an up-to-date, systematic and comprehensive presentation of theoretical results on waves and vibrations in quartz crystal plates. It expounds on the application of the theories of elasticity and piezoelectricity in acoustic wave devices made from crystal plates through a coverage spanning from classical results on acoustic wave resonators, up to present-day applications in acoustic wave sensors.This text begins with the exposition of the simplest thickness modes and various frequency effects in them due to electrodes, mass loading, contact with fluids, air gaps, etc., and continues on to the more complicated shear-horizontal modes, as well as straight-crested modes varying along the digonal axis of rotated Y-cut quartz. Modes varying in both of the in-plane directions of crystal plates are also addressed.The analysis within are based on the three-dimensional theories of piezoelectricity and anisotropic elasticity with various approximations when needed. Both free vibration modes (stationary waves) and propagating waves are studied in this text. Forced vibration is also treated in a few places.This book is intended to serve as an informative reference to personnel who employ piezoelectric crystal plates in the course of their profession.

This book presents macroscopic theories of magnetoelastic interactions in solids, mainly for saturated ferromagnetoelastic materials. In these materials, the distributed magnetic moments are aligned and have a fixed magnitude. A disturbance of the magnetic moments propagates as what is called spin waves. In elastic ferromagnets, acoustic waves may interact with spin waves, which is referred to as phonon-magnon interaction. Continuum modeling of magnetoelastic interactions in saturated ferromagnets has a few unique and interesting features. In addition to the magnetic body force and couple on the magnetic moments, the short-range interaction among neighboring magnetic moments may be described by distributed surface couples. This leads to a magnetization gradient theory. The angular momenta associated with the magnetic moments need to be considered for spin waves. In addition, the saturation condition on the magnetization vector functions as a constraint mathematically, which has important implications in the constitutive relations of these materials. The book discusses the relatively simple situation of rigid ferromagnets first and then proceeds to elastic ferromagnets. Thermal and dissipative effects as well as interactions with electromagnetic waves are also considered. Structural problems of elastic plates and beams with magnetoelastic interactions are treated as well.