Principios Mecatronicos

Mechatronics

SOLID MECHANICS AND ITS APPLICATIONS Volume 136
Series Editor: G.M.L. GLADWELL
Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI

Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving visionand insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; thetheories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others areaccessible to final year undergraduates; but essentially the emphasis is on readability and clarity.

For a list of related mechanics titles, see final pages.

Mechatronics
Dynamics of Electromechanical and Piezoelectric Systems
by

A. PREUMONT
ULB Active Structures Laboratory, Brussels, Belgium

A C.I.P. Catalogue record for this book is available from the Library of Congress.ISBN-10 ISBN-13 ISBN-10 ISBN-13

1-4020-4695-2 (HB) 978-1-4020-4695-7 (HB) 1-4020-4696-0 (e-book) 978-1-4020-4696-4 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com

Printed on acid-free paper

All Rights Reserved © 2006 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means,electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.

”

Tenez, mon ami, si vous y pensez bien, vous trouverez qu’en tout, notrev´ritable sentiment n’est pas celui e dans lequel nous n’avons jamais vacill´; e mais celui auquel nous sommes le plus habituellement revenus.”

Diderot, (Entretien entre D’Alembert et Diderot)

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1 Lagrangian dynamics of mechanical systems . . . . . . . . . . . 1.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Kinetic state functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Generalized coordinates, kinematic constraints . . . . . . . . . . . 1.3.1 Virtual displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 The principle of virtual work . . . . . . . . . . . .. . . . . . . . . . . . . . 1.5 D’Alembert’s principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Hamilton’s principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1 Lateral vibration of a beam . . . . . . . . . . . . . . . . . . . . . . 1.7 Lagrange’s equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.1 Vibration ofa linear, non-gyroscopic, discrete system 1.7.2 Dissipation function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7.3 Example 1: Pendulum with a sliding mass . . . . . . . . . 1.7.4 Example 2: Rotating pendulum . . . . . . . . . . . . . . . . . . . 1.7.5 Example 3: Rotating spring mass system . . . . . . . . . . 1.7.6 Example 4: Gyroscopic effects . . . . . . . . . . . . . . . . ....