Dynamics of structures

Dynamics of Structures

Third Edition

\

Dedicated to Yash

and ro

Rachna and Rajesh

Ahhinav and PriyaJ

Atnl and Deepali

and their children

who are a source of immense joy ro us

Dynamics of Structures

Third Edition

Jagmohan L. Humar

Carleton University, Ottawa, Canada

CRC Press

Taylor &. Francis Croup

Boca Raton London New York Leiden

CRC Press is an imprint of the

Taylor & Francis Croup, an informa business

A B A LK E M A B O O K

Cover information:

The picture of Confederation bridge on the cover is reproduced courtesy of Nicolas Raymond (www.devaintart

.com) who took the photograph. The bridge joins the eastern Canadian provinces of Prince Edward Island and New

Br unswick. The curved. 12.9 kilometre long bridge is the longest in the world crossing ice-covered water.

The insets show the mode shapes obtained from a finite element model of a typical span of the bridge (courtesy

Prof. David Lau, Carleton University).

C RC Press/Balkema is an imprint o f the Taylor & Francis Group,

an informa business

© 2012 T a ylo r & Francis G ro u p , London, U K

Typ eset by MPS Limited, a Macmillan Com pany, Chennai, India

Printed and bound in the USA by Edwards B ro th e rs. Inc, Lillington, N C

All rights reserved. No part of this publication or the information

contained herein may be reproddt^d, stored in a retrieva-l system,

or transm itted in any form or by any means: e le c tr^ tlc , mechanical,

by photocopying, recording or otherw ise, without wri4ten prior

perm ission from the publishers. • * t *

* %

Although all care is taken to ens,ure integrity anfl q u a lity of this

publication and the information herein, np responsibility is

assumed by the publishers nor the author for any damage to the

p ro p erty or persons as a result of operation or use of this

publication and/or the information contained herein.

Library of Congress Cataloging-m-Publication Data

Humar, J. L.

Dynam ics of stru ctu res / Jagmohan L. Hum ar. — 3rd ed.

p. cm.

"A Balkema Book.”

Includes bibliographical references and index.

ISBN 978-0-4 15-62086-4 (hardback : alk. paper)

I. Structural dynamics. I. Title.

TA654.H79 2012

6 2 4 .1 '7-dc23

2011046841

Published by: C R C Press/Balkema

P.O. Box 447, 2300 AK Leiden,The Netherlands

e-mail: [email protected]

www.crcpress.com - www.taylorandfrancis.co.uk - www.balkema.nl

ISBN: 978-0-415-62086-4 (Hbk)

ISBN: 978-0-203-1 1256-4 (eBook)

Contents

Preface

Preface to Second Edition

last of symbols

xv

xvii

xxi

I Introduction I

l.l Objectives of rhe study of structural dynamics 1

1.2 Importance of vibration analysis 2

1.3 Nature of exciting forces 3

1.3.1 Dynamic forces caused by rotating machinery J J \ * 0

3

1.3.2 Wind loads 4

r

^•

i

r

•

4^

Blast loads 4

1.3.4 Dynamic forces caused by earthquakes 5

1.3.5 Periodic and nonperiodic loads 7

1.3.6 Deterministic and nondeterministic loads 8

1.4 Mathematical modeling of'dynamic systems 1 7 / J 9

1.5 Systems of units •

1 1

1.6 Organization of the text 12

P A R T I

2 Formulation of the equations of motion:

Single-degree-of-freedom systems 19

2.1 Introduction 19

2.2 Inertia forces 19

2.3 Resultants of inertia forces on a rigid body 21

2.4 Spring forces 26

2.5 Damping forces 29

2.6 Principle of virtual displacement 31

2.7 Formulation of the equations of motion 35

2.7.1 Svstems with localized mass and localized stiffness

J

35

2.7.2 Svstems with localized mass but distributed stiffness

m

37

2.7.3 Svstems with distributed mass but localized stiffness 38

2.7.4 Systems with distributed stiffness and distributed mass 42

2.8 Modeling of multi-degree-of-freedom discrete parameter system 51

2.9 Effect of qravitv load 53