Structural Dynamics of Earthquake Engineering: Theory and Application using Mathematica and Matlab (Woodhead Publishing in Materials)

903 Pages·2009·14.79 MB·English

by  S. Rajasekaran

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Structural dynamics of earthquake engineering
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Structural
dynamics of
earthquake
engineering
Theory and application using
MATHEMATICA and MATLAB
S. Rajasekaran
CRC Press
Boca Raton Boston New York Washington, DC
W
OODHEAD PUBLISHING LIMITED
Oxford Cambridge New Delhi
iv
Published by Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington,
Cambridge CB21 6AH, UK
www.woodheadpublishing.com
Woodhead Publishing India Private Limited, G-2, Vardaan House, 7/28 Ansari Road,
Daryaganj, New Delhi – 110002, India
Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW,
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First published 2009, Woodhead Publishing Limited and CRC Press LLC
© 2009, Woodhead Publishing Limited
The author has asserted his moral rights.
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British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library.
Library of Congress Cataloging in Publication Data
A catalog record for this book is available from the Library of Congress.
Woodhead Publishing ISBN 978-1-84569-518-7 (book)
Woodhead Publishing ISBN 978-1-84569-573-6 (e-book)
CRC Press ISBN 978-1-4398-0132-1
CRC Press order number: N10026
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To my wife Saraswathi
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Contents
Programs available in this book xvii
Preface xxi
Acknowledgements xxiii
1 Introduction to dynamics 1
1.1 Introduction 1
1.2 Different types of dynamic loads 2
1.3 Difference between dynamic and static problems 2
1.4 Methodology 4
1.5 Types of vibration 5
1.6 Further reading 6
Part I Structural dynamics in relation to earthquakes
2 Free vibration of single-degree-of-freedom systems
(undamped) in relation to structural dynamics during
earthquakes 9
2.1 Introduction 9
2.2 Formulation of the equation of motion 9
2.3 Simple harmonic theory 10
2.4 Newton’s second law 14
2.5 Simple pendulum 19
2.6 Comparison of simple harmonic motion and uniform
circular motion 21
2.7 Energy method 22
2.8 Rayleigh method 24
2.9 D’Alembert’s principle 24
2.10 Free vibration of rigid bodies without damping 25
2.11 Program 2.1: MATLAB program to draw displacement,
velocity and acceleration with respect to time 28
viii Contents
2.12 Program 2.2: MATHEMATICA program to draw
displacement, velocity and acceleration with respect
to time 29
2.13 Free vibration of structural systems 32
2.14 Exercises 39
2.15 Further reading 42
3 Free vibration of single-degree-of-freedom systems
(under-damped) in relation to structural dynamics
during earthquakes 43
3.1 Introduction 43
3.2 Damping free vibrations 43
3.3 Logarithmic decrement 47
3.4 Hysteresis damaping 53
3.5 Coulomb damping 55
3.6 Numerical method to find response due to initial
conditions only 58
3.7 Program 3.1: MATLAB program for free vibration of
under-damped SDOF systems 59
3.8 Program 3.2: MATHEMATICA program for free
vibration of damped SDOF systems 60
3.9 Summary 66
3.10 Exercises 66
3.11 Further reading 67
4 Forced vibration (harmonic force) of single-degree-
of-freedom systems in relation to structural
dynamics during earthquakes 68
4.1 Forced vibration without damping 68
4.2 Beating phenomenon 73
4.3 Resonance 75
4.4 Forced vibration with damping 77
4.5 Program 4.1: MATHEMATICA program to find
displacement response of under-damped system
subjected to sinusoidal loading 79
4.6 Recurrence formula of Wilson 81
4.7 Program 4.2: MATLAB program for finding response
due to harmonic force 82
4.8 Vector relationship in forced vibration 83
4.9 Rotating imbalance 87
4.10 Transmissibility (force isolation) 92
4.11 Program 4.3: MATLAB program to compute MF,
MX/me and TR 93
Contents ix
4.12 Effectiveness of foundation 94
4.13 Displacement isolation 95
4.14 Vibration-measuring instruments 96
4.15 How to evaluate damping in SDOF 97
4.16 Response to ground acceleration 99
4.17 Exercises 101
4.18 Further reading 103
5 Response of structures to periodic dynamic loadings 105
5.1 Introduction 105
5.2 Fourier analysis 106
5.3 Program 5.1: MATHEMATICA program to determine
Fourier coefficients of forcing function 111
5.4 Response to periodic excitation 115
5.5 Program 5.2: MATHEMATICA program for finding the
response to a periodic function 116
5.6 Frequency domain analysis 121
5.7 Alternative form of Fourier series 122
5.8 Program 5.3: MATLAB program to evaluate amplitudes
and phase angles 124
5.9 Expression of forcing function using complex variable
approach 127
5.10 Discrete fourier transform (DFT) and fast fourier
transform (FFT) 131
5.11 Gibbs phenomenon 132
5.12 Summary 133
5.13 Exercises 133
5.14 Further reading 134
6 Response of structures to impulse loads 136
6.1 Introduction 136
6.2 Impulsive loading – sine wave 136
6.3 Program 6.1: MATLAB program to obtain maximum
response for half sine cycle pulse 140
6.4 Response to other arbitrary dynamic excitation 141
6.5 Duhamel integral 146
6.6 Response to arbitrary dynamic excitation 148
6.7 Response spectrum 157
6.8 Program 6.3: MATLAB program to find the response
spectrum for any load pulse 158
6.9 Laplace transform 163
6.10 Program 6.4: MATHEMATICA program for Laplace
transform method 165