Harris C.M., Piersol A.G. Harris Shock and vibration handbook
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HARRIS’
SHOCK AND
VIBRATION
HANDBOOK
Cyril M. Harris Editor
Charles Batchelor Professor Emeritus
of Electrical Engineering
Columbia University
New York, New York
Allan G. Piersol Editor
Consultant
Piersol Engineering Company
Woodland Hills, California
Fifth Edition
McGRAW-HILL
New York Chicago San Francisco Lisbon London Madrid
Mexico City Milan New Delhi San Juan Seoul
Singapore Sydney Toronto
8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page iii
Library of Congress Cataloging-in-Publication Data
Harris’ shock and vibration handbook / Cyril M. Harris, editor, Allan G.
Piersol, editor.—5th ed.
p. cm.
ISBN 0-07-137081-1
1. Vibration—Handbooks, manuals, etc. 2. Shock (Mechanics)—
Handbooks, manuals, etc. I. Harris, Cyril M., date. II. Piersol, Allan G.
TA355.H35 2002
620.3—dc21 2001044228
Copyright © 2002, 1996, 1988, 1976, 1961 by The McGraw-Hill Companies,
Inc. All rights reserved. Printed in the United States of America. Except as
permitted under the United States Copyright Act of 1976, no part of this pub-
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stored in a data base or retrieval system, without the prior written permission
of the publisher.
1234567890 DOC/DOC 07654321
ISBN 0-07-137081-1
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8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page iv
ABOUT THE EDITORS
Cyril M. Harris, one of the world’s leading authorities on shock, vibration, and
noise control, currently lectures at Columbia University where he is the Charles
Batchelor Professor Emeritus of Electrical Engineering. Dr. Harris has received
many honors for his scientific and engineering achievements, including membership
in both the National Academy of Sciences and the National Academy of Engineer-
ing. He has been the recipient of the Gold Medal and the Sabine Medal of the
Acoustical Society of America, the Franklin Medal of the Franklin Institute, the
Gold Medal of the Audio Engineering Society, and the A.I.A. Medal of the Ameri-
can Institute of Architects.
He received his Ph.D. degree in physics from M.I.T. and has been awarded hon-
orary doctorates by Northwestern University and the New Jersey Institute of Tech-
nology.Among books written or edited by Dr. Harris are the following McGraw-Hill
publications: Handbook of Acoustical Measurements and Noise Control, Third Edi-
tion (1991); Noise Control in Buildings (1994); Dictionary of Architecture and Con-
struction, Third Edition (2000); and Handbook of Utilities and Services for Buildings
(1990).
Allan G. Piersol is a professional engineer in private practice specializing in the
analysis of and design for shock, vibration, and acoustical environments. He received
an M.S. degree in engineering from UCLA and is licensed in both mechanical and
safety engineering. Mr. Piersol is a Fellow of the Acoustical Society of America and
the Institute of Environmental Sciences and Technology, and a recipient of the latter
organization’s Irvin Vigness Memorial Award. He is the co-author with Julius S.
Bendat of several books published by John Wiley & Sons, the most recent being
Engineering Applications of Correlation and Spectral Analysis, Second Edition
(1993), and Random Data: Analysis and Measurement Procedures, Third Edition
(2000). He is also a co-author of NASA-HDBK-7005, Dynamic Environmental Cri-
teria (2001), and a contributor to numerous other engineering handbooks.
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PREFACE
The first edition of the Shock and Vibration Handbook in 1961 brought together for
the first time a comprehensive survey of classical shock and vibration theory and
current applications of that theory to contemporary engineering practice. Edited by
Cyril M. Harris and the late Charles E. Crede, the book was translated into several
languages and became the standard reference work throughout the world. The Sec-
ond Edition appeared in 1976, the Third Edition in 1988, and the Fourth Edition in
1996.
There have been many important developments in the field since the Fourth
Edition was published, including advances in theory, new applications of computer
technologies, new methods of shock and vibration control, new instrumentation,
and new materials and techniques used in controlling shock and vibration. Many
new standards and test codes have also been enacted. These developments have
necessitated this Fifth Edition, which covers them all and presents a thorough,
unified, state-of-the-art treatment of the field of shock and vibration in a single
volume that is approximately 10 percent longer than its predecessor edition.A new
co-editor, highly regarded as an author in his own right, has collaborated with an
original editor in this endeavor. The book brings together a wide variety of skills
and expertise, resulting in the most significant improvements in the Handbook
since the First Edition.
New chapters have been added and many other chapters updated, revised, or
expanded to incorporate the latest developments. Several chapters written by
authors who are now deceased have been revised and updated by the editors, but the
credits to the original authors are retained in recognition of their outstanding con-
tributions to shock and vibration technology. (For convenience, and to retain as
closely as possible the chapter sequence of prior editions, several chapters have been
designated Part II or III of an associated chapter.) The editors have avoided dupli-
cation of content between chapters except when such repetition is advisable for rea-
sons of clarity. In general, chapters in related areas are grouped together whenever
possible. The first group of chapters presents a theoretical basis for shock and vibra-
tion. The second group considers instrumentation and measurement techniques, as
well as procedures for analyzing and testing mechanical systems subjected to shock
and vibration.The third group discusses methods of controlling shock and vibration,
and the design of equipment for shock and vibration environments. A final chapter
presents the effects of shock and vibration on human beings, summarizing the latest
findings in this important area. Extensive cross-references enable the reader to
locate relevant material in other chapters.The Handbook uses uniform terminology,
symbols, and abbreviations throughout, and usually both the U.S. Customary System
of units and the International System of units.
The 42 chapters have been written by outstanding authorities, all of them experts
in their fields. These specialists come from industrial organizations, government and
university laboratories, or consulting firms, and all bring many years of experience to
their chapters. They have made a special effort to make their chapters as accessible
xi
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as possible to the nonspecialist, including the use of charts and written explanations
rather than highly technical formulas when appropriate.
Over the decades, the Handbook has proven to be a valuable working reference
for those engaged in many areas of engineering, among them aerospace, automotive,
air-conditioning, biomedical, civil, electrical, industrial, mechanical, ocean, and
safety engineering, as well as equipment design and equipment maintenance engi-
neering. Although this book is not intended primarily as a textbook, it has been
adopted for use in many universities and engineering schools because its rigorous
mathematical basis, combined with its solutions to practical problems, are valuable
supplements to classroom theory.
We thank the contributors to the Fifth Edition for their skill and dedication in the
preparation of their chapters and their diligence in pursuing our shared objective of
making each chapter the definitive treatment in its field; in particular, we thank
Harry Himelblau for his many helpful suggestions. We also wish to express our
appreciation to the industrial organizations and government agencies with which
many of our contributors are associated for clearing for publication the material
presented in their chapters. Finally, we are indebted to the standards organizations
of various countries—particularly the American National Standards Institute
(ANSI), the International Standards Organization (ISO), and the International
Electrotechnical Commission (IEC)—as well as to their many committee members
whose selfless efforts have led to the standards cited in this Handbook.
The staff members of the professional book group at McGraw-Hill have done an
outstanding job in producing this new edition. We thank them all, and express our
special appreciation to the production manager,Tom Kowalczyk, for his support.
Cyril M. Harris
Allan G. Piersol
xii PREFACE
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CONTENTS
Chapter 1. Introduction to the Handbook 1.1
Cyril M. Harris, Charles Batchelor Professor Emeritus of Electrical Engineering, Columbia
University, New York, NY 10027.
Chapter 2. Basic Vibration Theory 2.1
Ralph E. Blake, formerly Consultant, Technical Center of Silicon Valley, San Jose, CA.
Chapter 3. Vibration of a Resiliently Supported Rigid Body 3.1
Harry Himelblau, Consultant, The Boeing Company, Space and Communications Division,
Canoga Park, CA 91309-7922.
AND
Sheldon Rubin, Consultant, Rubin Engineering Company, Sherman Oaks, CA 91403-4708.
Chapter 4. Nonlinear Vibration 4.1
Fredric Ehrich, Senior Lecturer, Massachusetts Institute of Technology, Cambridge, MA 02139.
AND
H. Norman Abramson, Retired Executive Vice President, Southwest Research Institute,
San Jose,TX 78228.
Chapter 5. Self-Excited Vibration 5.1
Fredric Ehrich, Senior Lecturer, Massachusetts Institute of Technology, Cambridge, MA 02139.
Chapter 6. Dynamic Vibration Absorbers and Auxiliary Mass Dampers 6.1
F. Everett Reed, formerly President, Littleton Research and Engineering Corporation,
Littleton, MA 01460.
Chapter 7. Vibration of Systems Having Distributed Mass and Elasticity 7.1
William F. Stokey, Late Professor of Mechanical Engineering, Carnegie-Mellon University,
Pittsburgh, PA 15236.
Chapter 8. Transient Response to Step and Pulse Functions 8.1
Robert S. Ayre, Late Professor of Civil Engineering, University of Colorado, Boulder,
CO 80309.
Chapter 9. Effect of Impact on Structures 9.1
William H. Hoppman II, Late Professor of Engineering, University of South Carolina,
Columbia, SC 29208.
v
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Chapter 10. Mechanical Impedance 10.1
Elmer L. Hixson, Professor Emeritus of Electrical Engineering, University of Texas at Austin,
Austin,TX 78712.
Chapter 11. Statistical Methods for Analyzing Vibrating Systems 11.1
Richard G. DeJong, Professor of Engineering, Calvin College, Grand Rapids, MI 49546.
Chapter 12. Vibration Transducers 12.1
Anthony S. Chu, Director of Marketing, Test Instrumentation, Endevco Corporation, San Juan
Capistrano, CA 92675.
Chapter 13. Vibration Measurement Instrumentation 13.1
Robert B. Randall, Associate Professor, University of New South Wales, Sydney, NSW 2052,
Australia.
Chapter 14. Vibration Analyzers and Their Use 14.1
Robert B. Randall, Associate Professor, University of New South Wales, Sydney, NSW 2052,
Australia.
Chapter 15. Measurement Techniques 15.1
Cyril M. Harris, Charles Batchelor Professor Emeritus of Electrical Engineering, Columbia
University, New York, NY 10027.
Chapter 16. Condition Monitoring of Machinery 16.1
Joëlle Courrech, Area Sales Manager, Brüel & Kjaer, Sound and Vibration Measurement,
A/S Denmark.
AND
Ronald L. Eshleman, Director, Vibration Institute,Willowbrook, IL 60514.
Chapter 17. Strain-Gage Instrumentation 17.1
Earl J. Wilson, formerly Chief of Strain and Environmental Branch, National Aeronautics and
Space Administration, Flight Research Center, Edwards AFB, CA 93524.
Chapter 18. Calibration of Pickups 18.1
M. Roman Serbyn, Associate Professor, Morgan State University, Baltimore, MD 21251.
AND
Jeffrey Dosch, Technical Director, PCB Piezotronics, Depew, NY 14043-2495.
Chapter 19. Shock and Vibration Standards 19.1
David J. Evans, Mechanical Engineer, National Institute of Standards and Technology,
Gaithersburg, MD 20899-9221.
AND
Henry C. Pusey, Executive Director, Society for Machinery Failure Prevention Technology,
Winchester, VA 22601-6354.
Chapter 20. Test Criteria and Specifications 20.1
Allan G. Piersol, Consultant, Piersol Engineering Company,Woodland Hills, CA 91364-4830.
vi CONTENTS
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Chapter 21. Experimental Modal Analysis 21.1
Randall J. Allemang, Professor of Structural Dynamics Research Laboratory, University of
Cincinnati, Cincinnati, OH 45221.
AND
David L. Brown, Professor of Structural Dynamics Research Laboratory, University of
Cincinnati, Cincinnati, OH 45221.
Chapter 22. Concepts in Vibration Data Analysis 22.1
Allan G. Piersol, Consultant, Piersol Engineering Company,Woodland Hills, CA 91364-4830.
Chapter 23. Concepts in Shock Data Analysis 23.1
Sheldon Rubin, Consultant, Rubin Engineering Company, Sherman Oaks, CA 91403-4708.
Chapter 24. Vibration of Structures Induced by Ground Motion 24.1
William J. Hall, Professor Emeritus of Civil Engineering, University of Illinois at Urbana-
Champaign, Urbana, IL 61801.
Chapter 25. Vibration Testing Machines 25.1
David O. Smallwood, Distinguished Member of the Technical Staff, Sandia National
Laboratories, Albuquerque, NM 87185.
Chapter 26, Part I. Shock Testing Machines 26.1
Richard H. Chalmers, Late Consulting Engineer, Induced Environments Consultants,
San Diego, CA 92107.
Chapter 26, Part II. Pyroshock Testing 26.15
Neil T. Davie, Principal Member of the Technical Staff, Sandia National Laboratories,
Albuquerque, NM 87185.
AND
Vesta I. Bateman, Principal Member of the Technical Staff, Sandia National Laboratories,
Albuquerque, NM 87185.
Chapter 27. Application of Digital Computers 27.1
Marcos A. Underwood, President, Tu’tuli Enterprises, Gualala, CA 95445.
Chapter 28, Part I. Matrix Methods of Analysis 28.1
Stephen H. Crandall, Ford Professor of Engineering Emeritus, Massachusetts Institute of
Technology, Cambridge, MA 02139.
AND
Robert B. McCalley, Jr., Retired Engineering Manager, General Electric Company,
Schenectady, NY 12309.
Chapter 28, Part II. Finite Element Models 28.29
Robert N. Coppolino, Principal Engineer, Measurement Analysis Corporation, Torrence,
CA 90505.
Chapter 29, Part I. Vibration of Structures Induced by Fluid Flow 29.1
Robert D. Blevins, Consultant, San Diego, CA 92103.
CONTENTS vii
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Chapter 29, Part II. Vibration of Structures Induced by Wind 29.21
Alan G. Davenport, Founding Director, Boundary Layer Wind Tunnel Laboratory, and
Professor Emeritus of Civil Engineering, University of Western Ontario, London, ON N6A 5B9,
Canada.
AND
Milos Novak, Late Professor of Civil Engineering, University of Western Ontario, London, ON
N6A 5B9, Canada.
Chapter 29, Part III. Vibration of Structures Induced by Sound 29.47
John F. Wilby, Consultant, Wilby Associates, Calabasas, CA 91302.
Chapter 30. Theory of Vibration Isolation 30.1
Charles E. Crede, Late Professor of Mechanical Engineering and Applied Mechanics,
California Institute of Technology, Pasadena, CA 91125.
AND
Jerome E. Ruzicka, formerly Barry Controls, Brighton, MA 02135.
Chapter 31. Theory of Shock Isolation 31.1
R. E. Newton, Late Professor of Mechanical Engineering, United States Naval Postgraduate
School, Monterey, CA 93943.
Chapter 32. Shock and Vibration Isolators and Isolation Systems 32.1
Romulus H. Racca, formerly Senior Staff Engineer, Barry Controls, Brighton, MA 02135.
AND
Cyril M. Harris, Charles Batchelor Professor Emeritus of Electrical Engineering, Columbia
University, New York, NY 10027.
Chapter 33. Mechanical Properties of Rubber 33.1
Ronald J. Schaefer, President, Dynamic Rubber Technology, Wadsworth, OH 44281.
Chapter 34. Engineering Properties of Metals 34.1
James E. Stallmeyer, Professor Emeritus of Civil Engineering, University of Illinois at Urbana-
Champaign, Urbana, IL 61801.
Chapter 35. Engineering Properties of Composites 35.1
Keith T. Kedward, Professor of Mechanical Engineering, University of California at Santa
Barbara, Santa Barbara, CA 93106-5070.
Chapter 36. Material Damping and Slip Damping 36.1
Lawrence E. Goodman, Late Professor of Mechanics and Recorder Professor of Civil
Engineering, University of Minnesota, Minneapolis, MN 55455.
Chapter 37. Applied Damping Treatments 37.1
David I. G. Jones, Consultant, D/Tech Systems, Chandler, AZ 85226.
Chapter 38. Torsional Vibration in Reciprocating
and Rotating Machines 38.1
Ronald L. Eshleman, Director, Vibration Institute,Willowbrook, IL 60514.
viii CONTENTS
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