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.

A thorough guide to the fundamental development of linear piezoelectricity for vibrations Vibrations of Linear Piezostructures is an introductory text that offers a concise examination of the general theory of vibrations of linear piezostructures. This important book brings together in one comprehensive volume the most current information on the theory for modeling and analysis of piezostructures. The authors explore the fundamental principles of piezostructures, review the relevant mathematics, continuum mechanics and elasticity, and continuum electrodynamics as they are applied to electromechanical piezostructures, and include the work that pertains to linear constitutive laws of piezoelectricity. The book addresses modeling of linear piezostructures via Newton’s approach and Variational Methods. In addition, the authors explore the weak and strong forms of the equations of motion, Galerkin approximation methods for the weak form, Fourier or modal methods, and finite element methods. This important book: Covers the fundamental developments to vibrational theory for linear piezostructures Provides an introduction to continuum mechanics, elasticity, electrodynamics, variational calculus, and applied mathematics Offers in-depth coverage of Newton’s formulation of the equations of motion of vibrations of piezo-structures Discusses the variational methods for generation of equations of motion of piezo-structures Written for students, professionals, and researchers in the field, Vibrations of Linear Piezostructures is an up-to-date volume to the fundamental development of linear piezoelectricity for vibrations from initial development to fully modeled systems using various methods.

This is the first book devoted to a systematic description of the linear theory of piezoelectric shells and plates theory. The book contains two parts. In the first part, the theories for electroelastic thin-walled elements of arbitrary form with different directions of preliminary polarization are presented in an easy form for practical use. The approximate methods for integrating the equations of piezoelectric shells and plates are developed and applied for solving some engineering problems. In the second part, the theory of piezoelectric shells and plates is substantiated by the asymptotic method. The area of applicability for different kinds of electroelastic shell theories is studied. A new problem concerning the electroelastic phenomena at the edge of a thin-walled element is raised and solved. The Theory of Piezoelectric Shells and Plates will be valuable to researchers working in the field of electroelasticity as well as to electrical and electronic engineers who use thin-walled piezoelements. It is also be helpful for students and post-graduates specializing in mechanics and for scientists concerning asymptotic methods.