Vibrations of mechanical systems with regular structure
Vibrations in systems with a periodic structure is the subject of many ongoing research activities. This work presents the analysis of such systems with the help of the theory of representation groups by finite element methods, dynamic Compliance and dyna
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Liudmila Ya. Banakh · Mark L. Kempner
Vibrations of Mechanical Systems with Regular Structure With 109 Figures
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Dr. Liudmila Ya. Banakh Mechanical Engineering Research Institute Mal. Kharitonjevsky Str. 4 101990 Moscow Russia [email protected] Series Editors V.I. Babitsky Department of Mechanical Engineering Loughborough University LE11 3TU Loughborough Leicestershire Great Britain
Prof. Mark L. Kempner Ezra Str. 24/5 76201 Rehovot Israel [email protected]
J. Wittenburg Universitat Karlsruhe (TH) Institute für Technishe Mechanik Kaiserstr. 12 76128 Karlsruhe Germany
ISSN 1612-1384 e-ISSN 1860-6237 ISBN 978-3-642-03125-0 e-ISBN 978-3-642-03126-7 DOI 10.1007/978-3-642-03126-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010928905 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
In this book, regular structures are defined as periodic structures consisting of repeated elements (translational symmetry) as well as structures with a geometric symmetry. Regular structures have for a long time been attracting the attention of scientists by the extraordinary beauty of their forms. They have been studied in many areas of science: chemistry, physics, biology, etc. Systems with geometric symmetry are used widely in many areas of engineering. The various kinds of bases under machines, cyclically repeated forms of stators, reduction gears, rotors with blades mounted on them, etc. represent regular structures. The study of real-life engineering structures faces considerable difficulties because they comprise a great number of working mechanisms that, in turn, consist of many different elastic subsystems and elements. The computational models of such systems represent a hierarchical structure and contain hundreds and thousands of parameters. The main problems in the analysis of such systems are the dimension reduction of model and revealing the dominant parameters that determine its dynamics and form its energy nucleus. The two most widely used approaches to the simulation of such systems are as follows: 1. Methods u
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