Structural Dynamics for the Practising Engineer

221 Pages·1986·7.591 MB·\221

by  H.M. Irvine (Author)

STRUCTURAL DYNAMICS
FOR THE PRACTISING
ENGINEER
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STRUCTURAL
DYNAMICS
FOR THE PRACTISING
ENGINEER
Max Irvine
Department of Structural Engineering,
University of New South Wales
Taylor & Francis
Taylor & Francis Group
LONDON AND NEW YORK
By Taylor & Francis
2 Park Square, Milton Park, Abingdon, Oxon, 0X14 4RN
First edition 1986
First published in paperback 1990
Reprinted 1993
Transferred to Digital Printing 2005
© 1986 H.M. Irvine
ISBN 0 419 15930 4 (HB)
ISBN 0 046 24007 1 (PB)
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The publisher makes no representation, express or implied, with
regard to the accuracy of the information contained in this book and
cannot accept any legal responsibility or liability for any errors or
omissions that may be made.
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data available
First of all one must observe that each pendulum has its own time
of vibration, so definite and determinate that it is not possible to
make it move with any other period than that which nature has
given it. On the other hand one can confer motion upon even a
heavy pendulum which is at rest simply by blowing against it. By
repeating these blasts with a frequency which is the same as that of
the pendulum one can impart considerable motion.
Galileo Galilei, Discorsi a Due
Nuove Scienze (1638)
v

Preface
This book has been written for practising engineers and senior under­
graduates. It grew out of a set of notes prepared for classes given to each
of these groups at different times of the academic year over the past several
years. Both groups seem to enjoy the material and find that the applications
are fairly direct.
Every engineering office or group needs people with a knowledge of the
basic principles of structural dynamics but, regrettably, not every office has
them. There is still a fairly widely held belief that structural dynamics is too
difficult to be part and parcel of the structural engineer’s technical arma­
ment. It is true that it is difficult to find adequate time in the normal
undergraduate programme to treat the subject in any detail: it may,
therefore, be introduced as a technical elective at undergraduate level or
find expression as a first-year graduate subject or as a continuing education
course for the profession. However, like any other branch of engineering
analysis, structural dynamics can be reduced to basic principles, and it is on
those principles, properly applied, that many decisions can be made.
Thus, the aim of this book is to demonstrate that it is possible to get good
information on the ramifications of the dynamic response of structural sys­
tems without going into any great detail, and without employing advanced
techniques of analysis. Nearly all systems can be reduced to equivalent
single-degree systems and the quality of the resulting information is often
entirely adequate for the purpose of decision making, given that a detailed
knowledge of the system properties and loading is impossible anyway.
Therefore, with the exception of the final chapter, where multi-degree-of-
freedom systems are introduced, only single-degree-of-freedom systems
have been considered.
The work is but an introduction. Accordingly, there is little that is new
in the treatment, although some exceptions to this may be found in the
numerical schemes described in Chapter 4. The book contains quite a lot
of examples that have been worked in some detail. Many of these are drawn
from practice. There are also exercises set at the end of each chapter. Where
appropriate, reference has been made to some of the standard works in the
field and a few papers and books dealing with specialised topics are cited,
but the reference list is not intended to be exhaustive.
H. M. Irvine
Acknowledgements
1 gratefully acknowledge the assistance of Ruth Rogan and Colin Wingrove,
who set the original script on the word processor. The figures were drawn
by Mun Wye Yuen. Mario Attard, Ross Clarke, Glenn Dominish, Ray
Lawther, Neil Mickleborough, Russell Staley, Weeks White and Peter
Zeman read parts of the text and offered suggestions.
The style of the work owes much to the influence of the author’s former
colleague, John M. Biggs, Emeritus Professor of Civil Engineering at the
Massachusetts Institute of Technology. To him and to Paul C. Jennings,
Professor of Civil Engineering at the California Institute of Technology, I
owe a debt of gratitude.
Figure 3.5 is reproduced by kind permission of Conoco (UK) Limited.
Contents
Preface page vii
Acknowledgements viii
List of tables xi
1 Physical concepts 1
1.1 Conservation of energy and Newton’s second law 1
1.2 Free vibrations 3
1.3 Response to a suddenly applied load 13
1.4 Concluding remarks 30
Problems 31
Theory of the single-degree-of-freedom oscillator 35
2.1 Free vibrations 35
2.1.1 The undamped system 40
2.1.2 The damped system 40
2.2 Response to simple forcing functions 46
2.2.1 Suddenly applied load of constant magnitude
and infinite duration 46
2.2.2 Suddenly applied load of constant magnitude
but finite duration 60
2.2.3 Other simple loading cases 62
2.2.4 Response to an impulse 64
2.3 Elasto-plastic response to a suddenly applied load of
constant magnitude 66
Problems 79
3 Resonance and related matters 83
3.1 Steady-state response to sinusoidal forcing 83
3.1.1 Properties of the dynamic amplification
factor 86
3.1.2 Properties of the phase angle 88
3.1.3 Energy relations 89
3.2 Transient response to sinusoidal forcing 95
3.3 Response to ground motion 100
3.4 Vibration transmission and isolation 107
Problems 109
ix