An Introduction to the Mathematical Theory of Dynamic Materials
This book gives a mathematical treatment of a novel concept in material science that characterizes the properties of dynamic materials—that is, material substances whose properties are variable in space and time. Unlike conventional composites&n
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Advances in Mechanics and Mathematics VOLUME 15 Series Editors: David Y. Gao Virginia Polytechnic Institute and State University, U.S.A. Ray W. Ogden University of Glasgow, U.K. Advisory Editors: I. Ekeland University of British Columbia, Canada S. Liao Shanghai Jiao Tung University, P.R. China K.R. Rajagopal Texas A&M University, U.S.A. T. Ratiu Ecole Polytechnique, Switzerland David J. Steigmann University of California, Berkeley, U.S.A. W. Yang Tsinghua University, P.R. China
AN INTRODUCTION TO THE MATHEMATICAL THEORY OF DYNAMIC MATERIALS By KONSTANTIN A. LURIE Worcester Polytechnic Institute, Worcester, MA
Library of Congress Control Number: 2006940343 ISBN-10: 0-387-38278-X
e-ISBN-10: 0-387-38280-1
ISBN-13: 978-0-387-38278-4
e-ISBN-13: 978-0-387-38280-7
Printed on acid-free paper.
AMS Subject Classifications: 35L05, 35L70, 49S05, 49K20, 78A40, 78A48 © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.
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To the memory of Ella
Contents
1
A General Concept of Dynamic Materials . . . . . . . . . . . . . . . . . 1 1.1 The idea and definition of dynamic materials . . . . . . . . . . . . . . . . 1 1.2 Two types of dynamic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Implementation of dynamic materials in electronics and optics 7 1.3.1 Ferroelectric and ferromagnetic materials . . . . . . . . . . . . . 7 1.3.2 Nonlinear optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Some applications of dynamic materials . . . . . . . . . . . . . . . . . . . . 11 1.5 Dynamic materials and vibrational mechanics . . . . . . . . . . . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2
An 2.1 2.2 2.3 2.4 2.5 2.6
Activated Elastic Bar: Effective Properties . . . . . . . . . . . . . Longitudinal vibrations of activated elastic bar . . . . . . . . . . . . . . The effective parameters of activated laminate . . . . . . . . . . . . . . The effective parameters: homogenization . . . . . . . . . . . . . . . . . . . The effective parameters: the Floquet theory . . . . . . . . . . . . . . . . The effective parameters: discussion . . . . . . . . . . . . . . . . . . . . . . . . Balance of energy in longitudinal wave propagation through an activated elastic bar . . . .
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