Finite Element Analysis of Rotating Beams Physics Based Interpolatio
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and
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Ranjan Ganguli
Finite Element Analysis of Rotating Beams Physics Based Interpolation
Foundations of Engineering Mechanics Series editors V.I. Babitsky, Loughborough, Leicestershire, UK Jens Wittenburg, Karlsruhe, Germany
More information about this series at http://www.springer.com/series/3582
Ranjan Ganguli
Finite Element Analysis of Rotating Beams Physics Based Interpolation
123
Ranjan Ganguli Department of Aerospace Engineering Indian Institute of Science Bengaluru, Karnataka India
ISSN 1612-1384 ISSN 1860-6237 (electronic) Foundations of Engineering Mechanics ISBN 978-981-10-1901-2 ISBN 978-981-10-1902-9 (eBook) DOI 10.1007/978-981-10-1902-9 Library of Congress Control Number: 2016947015 © Springer Science+Business Media Singapore 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media Singapore Pte Ltd.
Preface
Rotating beams are important mathematical models for structures such as helicopter rotor blades, wind turbine rotor blades, propellers, turbine blades and robotic manipulators. Therefore, the modeling and analysis of rotating beams is an important practical problem. The natural frequencies of the rotating beam should be kept away from multiples of the rotor speed. Therefore, accurate frequency prediction is important. Control of rotating beams requires the development of low-order models. This motivates the development of efficient mathematical models. Since the rotating beam equation does not have a simple exact solution, approximate methods such as Rayleigh–Ritz, Galerkin, and the finite element methods are widely used for the vibration analysis of rotating beams. This book provides an introduction to the finite element for rotating beams. A background on the Rayleigh–Ritz and Galerkin method is also provided. The first chapter gives a detailed introduction to the rotating beam equation and illustrates the Rayleigh–Ritz
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