Parametric Resonance in Dynamical Systems
Parametric Resonance in Dynamical Systems discusses the phenomenon of parametric resonance and its occurrence in mechanical systems,vehicles, motorcycles, aircraft and marine craft, and micro-electro-mechanical systems. The contributors provide an introdu
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Thor I. Fossen • Henk Nijmeijer Editors
Parametric Resonance in Dynamical Systems
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Editors Thor I. Fossen Department of Engineering Cybernetics Norwegian University of Science and Technology NO-7491 Trondheim Norway [email protected]
Henk Nijmeijer Department of Mechanical Engineering Eindhoven University of Technology PO Box 513 5600 MB Eindhoven The Netherlands [email protected]
ISBN 978-1-4614-1042-3 e-ISBN 978-1-4614-1043-0 DOI 10.1007/978-1-4614-1043-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011943003 © Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Parametric Resonance in Dynamical Systems contains a collection of contributions presented at an invited workshop with the same name held from June 22–26, 2011 in Longyearbyen, Svalbard, Norway. The subject of the book is parametric resonance in marine and mechanical systems with focus on detection, mathematical modeling, and control. The book contains new results on modeling, detection, and control of parametric resonance and it is a supplement to engineers who are familiar with nonlinear systems.
What is Parametric Resonance? Parametric resonance is a phenomenon not caused by external excitation, but by time-varying changes in the parameters. The archetypical example is the Mathieu– Hill equation: y¨ + a(t)y = 0 where a(t + T ) = a(t). If the period T or 2T is an integer multiple of the natural period N, a resonance occurs causing the origin to become unstable. Not only mechanical systems, vehicles, motorcycles, aircraft, and marine craft but also micro–electro-mechanical systems are prone to parametric resonance. Sparse offshore platforms and ships also exhibit parametric resonance. For ships, parametric resonance is known to occur in roll in certain conditions. The resulting heavy roll motion, which can reach 30–40 degrees of roll angle, may bring the vessel into conditions dangerous for the ship, the cargo, and the crew. Container ships, fishing vessels, and cruise ships are also known to be prone to parametric roll and several incidents have been reported with significant damage to cargo as well as structural damages for millions of dollars. The origin of this unstable motion is the
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