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Vibration of Continuous Systems 连续系统的振动.pdf

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    Contents
    Preface
    1 Introduction
    1.1 What Is a Continuous System?
    1.2 A Comparison of Frequencies Obtained from Continuous and Discrete Models
    1.3 A Preview of the Subsequent Chapters
    2 Transverse Vibrations of Strings
    2.1 Differential Equation of Motion
    2.2 Free Vibrations; Classical Solution
    2.3 Initial Conditions
    2.4 Consideration of Transverse Gravity
    2.5 Free Vibrations; Traveling Wave Solution
    2.6 Other End Conditions
    2.7 Discontinuous Strings
    2.8 Damped Free Vibrations
    2.9 Forced Vibrations; Eigenfunction Superposition Method
    2.10 Forced Vibrations; Closed Form Exact Solutions
    2.11 Energy Functionals for a String
    2.12 Rayleigh Method
    2.13 Ritz Method
    2.14 Large Amplitude Vibrations
    2.15 Some Concluding Remarks
    References
    Problems
    3 Longitudinal and Torsional Vibrations of Bars
    3.1 Equation of Motion for Longitudinal Vibrations
    3.2 Equation of Motion for Torsional Vibrations
    3.3 Free Vibration of Bars
    3.4 Other Solutions by Analogy
    3.5 Free Vibrations of Bars with Variable Cross-Section
    3.6 Forced Vibrations of Bars; Material Damping
    3.7 Energy Functionals and Rayleigh and Ritz Methods
    References
    Problems
    4 Beam Vibrations
    4.1 Equations of Motion for Transverse Vibrations
    4.2 Solution of the Differential Equation for Free Vibrations
    4.3 Classical Boundary Conditions—Frequencies and Mode Shares
    4.4 Other Boundary Conditions—Added Masses or Springs
    4.5 Orthogonality of the Eigenfunctions
    4.6 Initial Conditions
    4.7 Continuous and Discontinuous Beams
    4.8 Forced Vibrations
    4.9 Energy Functionals—Rayleigh Method
    4.10 Ritz Method
    4.11 Effects of Axial Forces
    4.12 Shear Deformation and Rotary Inertia
    4.13 Curved Beams—Equations of Motion
    4.14 Curved Beams—Vibration Analysis
    References
    Problems
    5 Membrane Vibrations
    5.1 Equation of Motion for Transverse Vibrations
    5.2 Free Vibrations of Rectangular Membranes
    5.3 Circular Membranes
    5.4 Annular and Sectorial Membranes
    5.5 Initial Conditions
    5.6 Forced Vibrations
    5.7 Energy Functionals; Rayleigh and Ritz Methods
    References
    Problems
    6 Plate Vibrations
    6.1 Equation of Motion for Transverse Vibrations
    6.2 Free Vibrations of Rectangular Plates; Exact Solutions
    6.3 Circular Plates
    6.4 Annular and Sectorial Plates
    6.5 Energy Functionals; Rayleigh and Ritz Methods
    6.6 Approximate Solutions for Rectangular Plates
    6.7 Other Free Vibration Problems for Plates According to Classical Plate Theory
    6.8 Complicating Effects in Plate Vibrations
    References
    Problems
    7 Shell Vibrations
    7.1 Introduction
    7.2 Equations of Motion for Shallow Shells
    7.3 Free Vibrations of Shallow Shells
    7.4 Equations of Motion for Circular Cylindrical Shells
    7.5 Solutions for Deep or Closed Circular Cylindrical Shells
    References
    Problems
    8 Vibrations of Three-Dimensional Bodies
    8.1 Equations of Motion in Rectangular Coordinates
    8.2 Exact Solutions in Rectangular Coordinates
    8.3 Approximate Solutions for Rectangular Parallelepipeds
    8.4 Exact Solutions in Cylindrical Coordinates
    8.5 Approximate Solutions for Solid Cylinders
    8.6 Approximate Solutions for Hollow Cylinders
    8.7 Other Three-Dimensional Bodies
    References
    Problems
    9 Vibrations of Composite Continuous Systems
    9.1 Differential Equation of a Laminated Body in Rectangular Coordinates
    9.2 Laminated Beams
    9.3 Laminated Thick Beams
    9.4 Beams with Tubular Cross-Sections
    9.5 Laminated Thin Curved Beams
    9.6 Laminated Thick Curved Beams
    9.7 Laminated Thin Plates
    9.8 Thick Plates
    9.9 Laminated Shallow Shells
    9.10 Laminated Thick Shallow Shells
    9.11 Laminated Cylindrical Shells
    9.12 Vibrations of Other Laminated Shells
    References
    Problems
    A: Summary of One Degree-of-Freedom Vibrations (with Viscous Damping)
    B: Bessel Functions: Some Useful Information
    C: Hyperbolic Functions: Some Useful Relations
    Index
    A
    B
    C
    D
    E
    F
    G
    H
    I
    K
    L
    M
    N
    O
    P
    Q
    R
    S
    T
    V
    W
    Y
    Z
    Vibrations of Continuous Systems
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    Vibrations of Continuous Systems Arthur W. Leissa, Ph.D. Mohamad S. Qatu, Ph.D. New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto
    Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher. ISBN: 978-0-07-145728-6 MHID: 0-07-145728-3 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-142682-4, MHID: 0-07-142682-5. All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefi t of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps. McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. To contact a representative please e-mail us at bulksales@mcgraw-hill.com. Information contained in this work has been obtained by The McGraw-Hill Companies, Inc. (“McGraw-Hill”) from sources believed to be reliable. However, neither McGraw-Hill nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw-Hill and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. TERMS OF USE This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGrawHill”) and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms. THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.
    About the Authors Arthur W. Leissa, Ph.D., is Professor Emeritus in the Mechanical Engineering Department at Ohio State University. A world-leading researcher in the vibrations of continuous systems, he has published more than 100 papers in this field. He is the author of two other books, Vibration of Plates and Vibration of Shells, which were reprinted in 1993 by the Acoustical Society of America as “classics in vibration,” and have been cited by others in publications hundreds of times. Dr. Leissa founded two biennial conferences: the Pan American Congress of Applied Mechanics (PACAM) in 1989 and the International Symposium on Vibrations of Continuous Systems (ISVCS) in 1997. From 1987 to 1988 he was President of the American Academy of Mechanics, and from 1993 to 2008 he served as Editor-in-Chief of Applied Mechanics Reviews, the top international journal publishing review articles in applied mechanics. Dr. Leissa is a member of the editorial boards of Journal of Sound and Vibration, International Journal of Mechanical Sciences, Composite Structures, and Journal of Vibration and Control. Mohamad S. Qatu, Ph.D., is a Professor of Mechanical Engineering at Mississippi State University. Prior to his academic career, he held consulting, senior research, and managerial positions at Ford Motor Company, Dana Corporation, Dresser Industries, and Honda North America. He is the author of Vibration of Laminated Shells and Plates and the co-author of two books on vehicle dynamics. Dr. Qatu has published more than 40 papers on the vibrations of continuous systems and a similar number in automotive engineering, and holds two patents. He is the Founder and Editor-in-Chief of the International Journal of Vehicle Noise and Vibration, and is a member of the editorial boards of Composite Structures, Journal of Vibration and Control, and SAE International Journal of Passenger Cars—Mechanical Systems. He is a Fellow of both ASME and SAE.
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    Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . 1 1.1 What Is a Continuous System? 1.2 A Comparison of Frequencies Obtained from . . . . . . . . . . . . 5 . . . . . . . 7 Continuous and Discrete Models 1.3 A Preview of the Subsequent Chapters 2 Transverse Vibrations of Strings Initial Conditions 2.1 Differential Equation of Motion 2.2 Free Vibrations; Classical Solution 2.3 2.4 Consideration of Transverse Gravity 2.5 Free Vibrations; Traveling Wave Solution 2.6 Other End Conditions 2.7 Discontinuous Strings 2.8 Damped Free Vibrations 2.9 Forced Vibrations; Eigenfunction . . . . . . . . . . . . . . . . 1 1 . . . . . . . . . . . . . 1 2 . . . . . . . . . . . 1 5 . . . . . . . . . . . . . . . . . . . . . . . . . 1 9 . . . . . . . . . 2 2 . . . . . 2 3 . . . . . . . . . . . . . . . . . . . . . 2 6 . . . . . . . . . . . . . . . . . . . . . 3 0 . . . . . . . . . . . . . . . . . . . 3 5 Superposition Method . . . . . . . . . . . . . . . . . . . . . 3 8 2.10 Forced Vibrations; Closed Form Exact Solutions 2.11 Energy Functionals for a String 2.12 Rayleigh Method 2.13 Ritz Method 2.14 Large Amplitude Vibrations 2.15 Some Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 8 . . . . . . . . . . . . . 5 7 . . . . . . . . . . . . . . . . . . . . . . . . . . 5 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1 . . . . . . . . . . . . . . . . 6 6 . . . . . . . . . . . . . . . . . 6 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 References Problems 3 Longitudinal and Torsional Vibrations of Bars . . . . 7 7 3.1 Equation of Motion for Longitudinal Vibrations 3.2 Equation of Motion for Torsional Vibrations 3.3 Free Vibration of Bars 3.4 Other Solutions by Analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 . . 8 0 . . . . . . . . . . . . . . . . . . . . . 8 3 . . . . . . . . . . . . . . . . 8 6 vii
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