Engineering vibration

721 Pages·19.821 MB·English

by  Inman, Daniel J

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ISBN-13: 978-0-273-76844-9
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Pearson International Edition 9 780273 768449
Engineering Vibration
Fourth Edition
DaniEl J. inman
University of Michigan
international Editions contributions by
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Delhi Technological University
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© Pearson Education Limited 2014
The rights of Daniel J. Inman to be identified as author of this work have been asserted by him in accordance with the Copyright,
Designs and Patents Act 1988.
Authorized adaptation from the United States edition, entitled Engineering Vibration, Fourth Edition, ISBN 978-0-13-287169-3, by
Daniel J. Inman, published by Pearson Education © 2014.
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ISBN 10: 0-273-76844-1
ISBN 13: 978-0-273-76844-9
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Contents
Preface 8
1 IntroductIon to VIbratIon and the free resPonse 13
1.1 Introduction to Free Vibration 14
1.2 Harmonic Motion 25
1.3 Viscous Damping 33
1.4 Modeling and Energy Methods 43
1.5 Stiffness 58
1.6 Measurement 70
1.7 Design Considerations 75
1.8 Stability 80
1.9 Numerical Simulation of the Time Response 84
1.10 Coulomb Friction and the Pendulum 93
Problems 107
MATLAB Engineering Vibration Toolbox 127
Toolbox Problems 128
2 resPonse to harmonIc excItatIon 129
2.1 Harmonic Excitation of Undamped Systems 130
2.2 Harmonic Excitation of Damped Systems 142
2.3 Alternative Representations 156
2.4 Base Excitation 163
2.5 Rotating Unbalance 172
2.6 Measurement Devices 178
3
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4 Contents
2.7 Other Forms of Damping 182
2.8 Numerical Simulation and Design 192
2.9 Nonlinear Response Properties 200
Problems 209
MATLAB Engineering Vibration Toolbox 226
Toolbox Problems 226
3 General forced resPonse 228
3.1 Impulse Response Function 229
3.2 Response to an Arbitrary Input 238
3.3 Response to an Arbitrary Periodic Input 247
3.4 Transform Methods 254
3.5 Response to Random Inputs 259
3.6 Shock Spectrum 267
3.7 Measurement via Transfer Functions 272
3.8 Stability 274
3.9 Numerical Simulation of the Response 279
3.10 Nonlinear Response Properties 291
Problems 299
MATLAB Engineering Vibration Toolbox 313
Toolbox Problems 313
4 multIPle-deGree-of-freedom systems 315
4.1 Two-Degree-of-Freedom Model (Undamped) 316
4.2 Eigenvalues and Natural Frequencies 330
4.3 Modal Analysis 344
4.4 More Than Two Degrees of Freedom 352
4.5 Systems with Viscous Damping 368
4.6 Modal Analysis of the Forced Response 374
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Contents 5
4.7 Lagrange’s Equations 381
4.8 Examples 389
4.9 Computational Eigenvalue Problems for Vibration 401
4.10 Numerical Simulation of the Time Response 419
Problems 427
MATLAB Engineering Vibration Toolbox 445
Toolbox Problems 445
5 desIGn for VIbratIon suPPressIon 447
5.1 Acceptable Levels of Vibration 448
5.2 Vibration Isolation 454
5.3 Vibration Absorbers 467
5.4 Damping in Vibration Absorption 475
5.5 Optimization 483
5.6 Viscoelastic Damping Treatments 491
5.7 Critical Speeds of Rotating Disks 497
Problems 503
MATLAB Engineering Vibration Toolbox 513
Toolbox Problems 513
6 dIstrIbuted-Parameter systems 514
6.1 Vibration of a String or Cable 516
6.2 Modes and Natural Frequencies 520
6.3 Vibration of Rods and Bars 531
6.4 Torsional Vibration 537
6.5 Bending Vibration of a Beam 544
6.6 Vibration of Membranes and Plates 556
6.7 Models of Damping 562
6.8 Modal Analysis of the Forced Response 568
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6 Contents
Problems 578
MATLAB Engineering Vibration Toolbox 584
Toolbox Problems 584
7 VIbratIon testInG and exPerImental modal analysIs 585
7.1 Measurement Hardware 587
7.2 Digital Signal Processing 591
7.3 Random Signal Analysis in Testing 596
7.4 Modal Data Extraction 600
7.5 Modal Parameters by Circle Fitting 603
7.6 Mode Shape Measurement 608
7.7 Vibration Testing for Endurance and Diagnostics 618
7.8 Operational Deflection Shape Measurement 621
Problems 623
MATLAB Engineering Vibration Toolbox 627
Toolbox Problems 628
8 fInIte element method 629
8.1 Example: The Bar 631
8.2 Three-Element Bar 637
8.3 Beam Elements 642
8.4 Lumped-Mass Matrices 650
8.5 Trusses 653
8.6 Model Reduction 658
Problems 661
MATLAB Engineering Vibration Toolbox 668
Toolbox Problems 668
aPPendIx a comPlex numbers and functIons 669
aPPendIx b laPlace transforms 675
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Contents 7
aPPendIx c matrIx basIcs 680
aPPendIx d the VIbratIon lIterature 692
aPPendIx e lIst of symbols 694
aPPendIx f codes and Web sItes 699
aPPendIx G enGIneerInG VIbratIon toolbox
and Web suPPort 700
references 702
ansWers to selected Problems 704
Index 711
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Preface
This book is intended for use in a first course in vibrations or structural d ynamics
for undergraduates in mechanical, civil, and aerospace engineering or engineer-
ing mechanics. The text contains the topics normally found in such courses
in accredited engineering departments as set out initially by Den Hartog and
refined by Thompson. In addition, topics on design, measurement, and computa-
tion are addressed.
Pedagogy
Originally, a major difference between the pedagogy of this text and competing
texts is the use of high level computing codes. Since then, the other authors of
vibrations texts have started to embrace use of these codes. While the book is
written so that the codes do not have to be used, I strongly encourage their use.
These codes (Mathcad®, MATLAB®, and Mathematica®) are very easy to use,
at the level of a programmable calculator, and hence do not require any prereq-
uisite courses or training. Of course, it is easier if the students have used one or
the other of the codes before, but it is not necessary. In fact, the MATLAB®
codes can be copied directly and will run as listed. The use of these codes greatly
enhances the student’s understanding of the fundamentals of vibration. Just as
a picture is worth a thousand words, a numerical simulation or plot can enable a
completely dynamic understanding of vibration phenomena. Computer calcula-
tions and simulations are presented at the end of each of the first four chapters.
After that, many of the problems assume that codes are second nature in solving
vibration problems.
Another unique feature of this text is the use of “windows,” which are
distributed throughout the book and provide reminders of essential informa-
tion pertinent to the text material at hand. The windows are placed in the text at
points where such prior information is required. The windows are also used to
summarize essential information. The book attempts to make strong connections
to previous course work in a typical engineering curriculum. In particular, refer-
ence is made to calculus, differential equations, statics, dynamics, and strength of
materials course work.
8
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Preface 9
WHAT’S NEW IN THIS EDITION
Most of the changes made in this edition are the result of comments sent to me by
students and faculty who have used the 3rd edition. These changes consist of improved
clarity in explanations, the addition of some new examples that clarify concepts, and
enhanced problem statements. In addition, some text material deemed outdated and
not useful has been removed. The computer codes have also been updated. However,
software companies update their codes much faster than the publishers can update
their texts, so users should consult the web for updates in syntax, commands, etc. One
consistent request from students has been not to reference data appearing previously in
other examples or problems. This has been addressed by providing all of the relevant
data in the problem statements. Three undergraduate engineering students (one in
Engineering Mechanics, one in Biological Systems Engineering, and one in Mechanical
Engineering) who had the prerequisite courses, but had not yet had courses in vibra-
tions, read the manuscript for clarity. Their suggestions prompted us to make the fol-
lowing changes in order to improve readability from the student’s perspective:
Improved clarity in explanations added in 47 different passages in the text. In
addition, two new windows have been added.
Twelve new examples that clarify concepts and enhanced problem statements
have been added, and ten examples have been modified to improve clarity.
Text material deemed outdated and not useful has been removed. Two sections
have been dropped and two sections have been completely rewritten.
All computer codes have been updated to agree with the latest syntax changes
made in MATLAB, Mathematica, and Mathcad.
Fifty-four new problems have been added and 94 problems have been modi-
fied for clarity and numerical changes.
Eight new figures have been added and three previous figures have been modified.
Four new equations have been added.
Chapter 1: Changes include new examples, equations, and problems. New textual
explanations have been added and/or modified to improve clarity based on student sug-
gestions. Modifications have been made to problems to make the problem statement
clear by not referring to data from previous problems or examples. All of the codes have
been updated to current syntax, and older, obsolete commands have been replaced.
Chapter 2: New examples and figures have been added, while previous exam-
ples and figures have been modified for clarity. New textual explanations have also
been added and/or modified. New problems have been added and older problems
modified to make the problem statement clear by not referring to data from previ-
ous problems or examples. All of the codes have been updated to current syntax,
and older, obsolete commands have been replaced.
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