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- lication may be reproduced or distributed in any form or by any means, or 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 The sponsoring editor for this book was Kenneth P. McCombs, the editing supervisor was Stephen M. Smith, and the production supervisor was Sherri Souffrance. It was set in Times Roman by North Market Street Graphics. Printed and bound by R. R. Donnelley & Sons Company. McGraw-Hill books are available at special quantity discounts to use as pre- miums and sales promotions, or for use in corporate training programs. For more information, please write to the Director of Special Sales, McGraw-Hill Professional, Two Penn Plaza, New York, NY 10121-2298. Or contact your local bookstore. This book is printed on acid-free paper. 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 infor- mation published herein and neither McGraw-Hill nor its authors shall be responsible for any errors, omissions, or dam- ages arising out of use of this information. This work is pub- lished 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. 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. 8434_Harris_index_b.qxd 09/20/2001 12:20 PM Page 23 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page xi 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page xii 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page v 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page vi 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page vii 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 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page viii Chapter 39, Part I. Balancing of Rotating Machinery 39.1 Douglas G. Stadelbauer, formerly Executive Vice President, Schenck-Trebel Corporation, Deer Park, NY 11729. Chapter 39, Part II. Shaft Misalignment of Rotating Machinery 39.37 John D. Piotrowski, President, Turvac, Inc., Oregonia, OH 45054. Chapter 40. Machine-Tool Vibration 40.1 Eugene I. Rivin, Professor, Wayne State University, Detroit, MI 48202. Chapter 41. Equipment Design 41.1 Karl A. Sweitzer, Senior Systems Engineer, Eastman Kodak Company, Rochester, NY 14653-7214. AND Charles A. Hull, Staff Engineer, Lockheed Martin Corporation, Syracuse, NY 13221-4840. AND Allan G. Piersol, Consultant, Piersol Engineering Company, Woodland Hills, CA 91364-4830. Chapter 42. Effects of Shock and Vibration on Humans 42.1 Henning E. von Gierke, Director Emeritus, Biodynamics and Bioengineering Division, Armstrong Laboratory, Wright-Patterson AFB, OH 45433-7901. AND Anthony J. Brammer, Senior Research Officer, Institute for Microstructural Sciences, National Research Council, Ottawa, ON K1A 0R6, Canada. Index follows Chapter 42 CONTENTS ix 8434_Harris_fm_b.qxd 09/20/2001 11:40 AM Page ix [...]... ONE 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 13 1. 13 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 14 1. 14 CHAPTER ONE 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 15 1. 15 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 16 1. 16 CHAPTER ONE APPENDIX 1. 2 TERMINOLOGY For convenience, definitions of terms which are used frequently in the field of shock and vibration are assembled here Many of... and uniformly distributed load Thin flat plates of uniform thickness Miscellaneous systems The data for beams and plates are abstracted from Chap 7 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 10 1. 10 CHAPTER ONE 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 11 INTRODUCTION TO THE HANDBOOK 1. 11 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 12 1. 12 CHAPTER ONE 8434_Harris_ 01_ b.qxd 09/20/20 01. .. Rotational Velocity and Acceleration rad/sec rad/sec2 degree/sec degree/sec2 rev/sec rev/sec2 rev/min rev/min/sec → Multiply Value in → or → By To obtain value in ↓ rad/sec rad/sec2 degree/sec degree/sec2 1 57.30 0. 017 45 1 6.283 360 rev/sec rev/sec2 0 .15 92 0.00278 1 rev/min rev/min/sec 9.549 0 .16 67 60 0 .10 47 6.00 0. 016 7 1 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 38 AM Page 1. 9 1. 9 INTRODUCTION TO THE HANDBOOK motion... in Table 1. 3 for ready reference TABLE 1. 3 Conversion Factors for Simple Harmonic Motion Amplitude → Multiply numerical value in terms of → By To obtain value in terms of ↓ Average value Root-meansquare (rms) value Peak-to-peak value Amplitude 1 1.5 71 1. 414 0.500 Average value 0.637 1 0.900 0. 318 Root-meansquare (rms) value 0.707 1. 111 1 0.354 2.000 3 .14 2 2.828 1 Peak-to-peak value APPENDIX 1. 1 NATURAL... TABLE 1. 1 Conversion Factors for Translational Velocity and Acceleration Multiply Value in → or → By To obtain value in ↓ ft/sec ft/sec2 in./sec in./sec2 cm/sec cm/sec2 m/sec m/sec2 1 0.0 311 0.00259 0.0 010 2 0 .10 2 1 0.0833 0.0328 3.28 39.37 → g-sec, g g-sec, g ft/sec ft/sec2 32 .16 in./sec in./sec2 386 12 .0 1 0.3937 cm/sec cm/sec2 980 30.48 2.540 1 0.0254 0. 010 m/sec m/sec2 9.80 0.3048 10 0 1 TABLE 1. 2... application of impact or shock More frequently, however, shock and vibration are unwanted Then the objective is to eliminate or reduce their severity or, alternatively, to design equipment to withstand their influences These procedures are embodied in the control of shock and vibration Methods of control are emphasized throughout this Handbook CONTROL OF SHOCK AND VIBRATION Methods of shock and vibration control... impedance.) impedance Impulse is the productt of a force and the time during which the force is applied; 2 more specifically, the impulse is Fdt where the force F is time dependent and equal to zero before time t1 and after time t2 t1 impulse ͵ 8434_Harris_ 01_ b.qxd 09/20/20 01 11: 39 AM Page 1. 21 INTRODUCTION TO THE HANDBOOK impulse response function 1. 21 See Eq ( 21. 7) Induced environments are those conditions...8434_Harris_ 01_ b.qxd 09/20/20 01 11: 38 AM Page 1. 1 CHAPTER 1 INTRODUCTION TO THE HANDBOOK Cyril M Harris CONCEPTS OF SHOCK AND VIBRATION Vibration is a term that describes oscillation in a mechanical system It is defined by the frequency (or frequencies) and amplitude Either the motion of a physical object or structure or, alternatively, an oscillating force applied to a mechanical system is vibration. .. superposition of two simple harmonic quantities of different frequencies f1 and f2 They involve the periodic increase and decrease of amplitude at the beat frequency (f1 − f2) beats broadband random vibration Broadband random vibration is random vibration having its frequency components distributed over a broad frequency band (See random vibration. ) calibration factor The average sensitivity of a transducer... special vibration problems associated with the design and operation of machine tools Chapter 41 describes procedures for the design of equipment to withstand shock and vibration both the design and practical aspects A comprehensive up-to-date discussion of the human aspects of shock and vibration is considered in Chap 42, which describes the effects of shock and vibration on people SYMBOLS AND ACRONYMS . ↓ Amplitude 1 1.5 71 1. 414 0.500 Average value 0.637 1 0.900 0. 318 Root-mean- square (rms) 0.707 1. 111 1 0.354 value Peak-to-peak 2.000 3 .14 2 2.828 1 value motion having a frequency f of 50 Hz and a. ↓ g-sec, 1 0.0 311 0.00259 0.0 010 2 0 .10 2 g ft/sec 32 .16 1 0.0833 0.0328 3.28 ft/sec 2 in./sec 386 12 .0 1 0.3937 39.37 in./sec 2 cm/sec 980 30.48 2.540 1 100 cm/sec 2 m/sec 9.80 0.3048 0.0254 0. 010 1 m/sec 2 The. (20 01) , and a contributor to numerous other engineering handbooks. 8434_Harris_index_b.qxd 09/20/20 01 12:20 PM Page 23 PREFACE The first edition of the Shock and Vibration Handbook in 19 61 brought