Vibrations of Thick Cylindrical Structures
Due to strong potential applications and more demanding requirements imposed on long and thick cylindrical structures, there has been increased research and development activities during recent years in the field of vibration and passive vibration control
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Vibrations of Thick Cylindrical Structures
Vibrations of Thick Cylindrical Structures
Hamid R. Hamidzadeh ยท Reza N. Jazar
Vibrations of Thick Cylindrical Structures
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Hamid R. Hamidzadeh Department of Mechanical Engineering Tennessee State University 3500 John A. Merritt Blvd. Nashville TN 37209-1561 USA [email protected]
Reza N. Jazar Department of Mechanical and Automotive Engineering School of Aerospace, Mechanical and Manufacturing Engineering RMIT University Melbourne, VIC 3083 Australia [email protected]
ISBN 978-0-387-75590-8 e-ISBN 978-0-387-75591-5 DOI 10.1007/978-0-387-75591-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2009937454 c Springer Science+Business Media, LLC 2010 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. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Contents 1 Introduction 1.1 Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Vibrations of Cylindrical Structures . . . . . . . . . . . . 1.3 Vibrations of Thin Shell Cylinders . . . . . . . . . . . . . 1.4 Vibrations of Rods . . . . . . . . . . . . . . . . . . . . . . 1.5 Vibration of Thick Cylindrical Structures . . . . . . . . . 1.6 Vibrations of Damped Cylindrical Structures . . . . . . . 1.7 Vibration of Multilayered Cylindrical Structures . . . . . 1.8 Vibrations of Constrained Layered Cylindrical Structures 1.9 Vibrations of Cylindrical Panels . . . . . . . . . . . . . . .
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1 1 2 3 4 5 7 8 10 12
2 Governing Equations 2.1 State of Stresses at a Point . . . . . . . . 2.2 Equilibrium Equations in Terms of Stress 2.3 Stress-Strains Relationships . . . . . . . . 2.4 Strain-Displacement Relationships . . . . 2.5 Stress-Displacement Relationships . . . . 2.6 Equations of Motion . . . . . . . . . . . . 2.7 Key Symbols . . . . . . . . . . . . . . . .
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15 16 17 18 20 25 26 27
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3 Vibration of Single-Layer Cylinder 3.1 Governing Equation . . . . . . . . . . . . . . . . . . . . . . 3.2 Proposed Solution . . . . . . . . . . . . . . . . . . . . . . . 3.3 Derivation of Wave Equation . . . . . . . . . . . . . . . . . 3.4 Solutions to the Wave Equations . . . . . . . . . . . . . . . 3.
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