Structural dynamics of earthquake engineering: Theory and application using Mathematica and Matlab

902 Pages·2009·8.993 MB·English

by  Sekaran Rajasekaran

i
Structural dynamics of earthquake engineering
ii
Related titles:
Analysis and design of plated structures Volume 1: Stability
(ISBN 978-1-85573-967-3)
Steel-plated structures are used in a variety of marine and land-based applications,
such as ships, off-shore platforms, power and chemical plants, box-girder cranes and
bridges. This first volume in a two-volume sequence considers the various types of
buckling that plated structures are likely to encounter. Chapters also review buckling
in a range of materials from steel to differing types of composite. The book discusses
the behaviour of differing types of components used in steel-plated structures as well
as curved, stiffened, corrugated, laminated and other types of plate design. Together
with its companion volume, this is an essential reference in the design, construction
and maintenance of plated structures.
Analysis and design of plated structures Volume 2: Dynamics
(ISBN 978-1-84569-116-5)
This second of two volumes on plated structures reviews dynamics, particularly
vibration. Chapters review the behaviour of components such as beams and plates
together with materials such as steel, ceramic–metal and other composites. Together
with its companion volume, this important book summarises the wealth of research on
understanding the behaviour of thin-walled (plated) components. It is an invaluable
resource for all those concerned with the design, construction and service life of
plated structures.
Multiscale materials modelling: fundamentals and applications
(ISBN 978-1-84569-071-7)
The survival and success of many future industries relies heavily on engineered
materials and products with improved performance available at relatively low cost.
This demands not only the rapid development of new/improved processing techniques
but also a better understanding and control of the materials themselves, their structure
and properties. The aim of multiscale modelling is to predict the behaviour of
materials from their fundamental atomic structure. This emerging technique is
revolutionising our understanding of material properties and how they can be altered.
This important book reviews both the principles of multiscale materials modelling and
the ways it can be applied to understand and improve the performance of structural
materials.
Details of these and other Woodhead Publishing materials books can be obtained by:
• visiting our web site at www.woodheadpublishing.com
• contacting Customer Services (e-mail: [email protected];
fax: [phone]; tel.: [phone] ext. 130; address: Woodhead
Publishing Limited, Abington Hall, Granta Park, Great Abington, Cambridge CB21
6AH, UK)
If you would like to receive information on forthcoming titles, please send your
address details to: Francis Dodds (address, tel. and fax as above; e-mail:
[email protected]). Please confirm which subject areas you are
interested in.
iii
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,
Suite 300, Boca Raton, FL 33487, USA
First published 2009, Woodhead Publishing Limited and CRC Press LLC
© 2009, Woodhead Publishing Limited
The author has asserted his moral rights.
This book contains information obtained from authentic and highly regarded sources.
Reprinted material is quoted with permission, and sources are indicated. Reasonable efforts
have been made to publish reliable data and information, but the author and the publishers
cannot assume responsibility for the validity of all materials. Neither the author nor the
publishers, nor anyone else associated with this publication, shall be liable for any loss,
damage or liability directly or indirectly caused or alleged to be caused by this book.
Neither this book nor any part may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, microfilming and recording, or
by any information storage or retrieval system, without permission in writing from
Woodhead Publishing Limited.
The consent of Woodhead Publishing Limited does not extend to copying for general
distribution, for promotion, for creating new works, or for resale. Specific permission must
be obtained in writing from Woodhead Publishing Limited for such copying.
Trademark notice: Product or corporate names may be trademarks or registered trademarks,
and are used only for identification and explanation, without intent to infringe.
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
Thepublishers’ policy is to use permanent paper from mills that operate a
sustainable forestry policy, and which has beenmanufacturedfrompulp
which is processed using acid-free and elemental chlorine-free practices.
Furthermore, the publishers ensure that the text paper and cover board used
havemet acceptable environmental accreditation standards.
Typeset by Replika Press Pvt Ltd, India
Printed by TJ International Limited, Padstow, Cornwall, UK
v
To my wife Saraswathi
vi
vii
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
x Contents
6.11 Summary 167
6.12 Exercises 167
6.12 Further reading 169
7 Dynamic response of structures using numerical
methods 171
7.1 Introduction 171
7.2 Time stepping methods 172
7.3 Types of time stepping method 173
7.4 Response to base excitation 211
7.5 Wilson’s procedure (recommended) 217
7.6 Response of elasto-plastic SDOF system 224
7.7 Program 7.10: MATLAB program for dynamic response
for elasto-plastic SDOF system 227
7.8 Response spectra by numerical integration 231
7.9 Numerical method for evaluation of the Duhamel integral 232
7.10 Selection of direct integration method 236
7.11 Summary 237
7.12 Exercises 237
7.13 Further reading 238
8 Generalized coordinates and energy methods in
relation to structural dynamics during earthquakes 240
8.1 Introduction 240
8.2 Principle of virtual work 240
8.3 Generalized SDOF system: rigid bodies 241
8.4 Systems having distributed stiffness and distributed mass 243
8.5 Rayleigh method 248
8.6 Improved Rayleigh method 250
8.7 Hamilton’s principle 251
8.8 Lagrange’s equations 253
8.9 Computer-generated Euler–Lagrange equations using
MATHEMATICA 259
8.10 Summary 262
8.11 Exercises 263
8.12 Further reading 264
9 Two-degrees-of-freedom linear system response of
structures 266
9.1 Overview 266
9.2 Free vibration of undamped two-degrees-of-freedom system 266
9.3 Program 9.1: MATHEMATICA program to solve coupled
differential equations 273