Vibration of Structures and Machines: Practical Aspects PDF
Preview Vibration of Structures and Machines: Practical Aspects
Vibration of Structures and Machines Third Edition Springer Science+ Business Media, LLC Giancarlo Genta Vibration of Structures and Machines - - Practical Aspects Third Edition With 173 Illustrations , Springer Giancarlo Genta Dipartimento di Meccanica Politecnico di Torino Corso Duca degli Abruzzi, 24 10129 Torino ltaly Cover illustration: See Figure 4.34 for details. Library of Congress CataIoging-in-Publication Data Genla, G. (Giancarlo) Vibration of structures and machines: practical aspects I Giancarlo Genta. - 3rd ed. p. cm. Includes bibliographical references and index. ISBN 978-1-4612-7149-9 ISBN 978-1-4612-1450-2 (eBook) DOI 10.1007/978-1-4612-1450-2 I. Vibration-Mathematical models. 2. Structural dynamics. 3. Machinery-Vibration. I. Title. TA355.G44 1998 62 1.8' 1I-dc21 98-48084 Printed on acid-free paper. © 1999, 1995, 1993 Springer Science+Business Media New York Originally published by Springer-Verlag New York,lnc.in 1999 Softcover reprint of the hardcover 3rd edition 1999 All rights reserved. Tbis work may not be translated or copied in whole or in part without the written permission of the publisher ( Springer Science+Business Media, LLC ), 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. Tbe use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Timothy Taylor; manufacturing supervised by Jacqui Ashri. Camera-ready copy supplied by the author. 9 8 7 6 5 4 3 2 1 ISBN 978-1-4612-7149-9 To Franca and Alessandro Preface to the third edition Whenasked toprepareathirdeditionofthe currentbook,the author realized that come changes were needed. The first change is a formal one; it regards notation for matri ces and vectors. In earlier editions they were written using square brackets and braces, which are now dropped and replaced with bold characters. This type ofnotation is simpler and graphically cleaner, but it can be confusing to some students. The decision to do this was not an easy one, but it was made mostly because almost all recent books use this convention. This led to the need to change a few symbols to maintain a distinction between vectors, written with lower case letters, and matrices, for which capital letters are used. More substantial changes deal with a greater integration on the classical approach to mechanics of vibrations with that typical of system dynamics and control theory. Altough this book has not the aim of dealing with control systems in any detailed way, the recent experience of the author in the new Mechatronics Laboratory of Politecnicodi Torinoled to the suggestionoflooking at some aspects ofvibration dynamics in a more interdisciplinary way. G. Genta Torino, September 1998 Preface to the second edition This second edition follows the fust by about two years. Apart from correcting a number of printing errors, few additions have been in troduced. In the chapter on the finite element method, a short summary on finite elements in time (four-dimensional finite elements) has been introduced. In the chapter onrotordynamics, twonew graphicalrep resentations are used, namely, the roots locus plot for free whirling and a tridimensional plot for the forced response for which the des ignation of "orbital tubes" has been proposed. The former has been borrowedfrom controlled systems dynamics, where it is widely used, while the latter is made practical by the availability of powerful graphical tools for postprocessing numericalor experimentalresults. As a last point, a more detailed description of the behaviour of magnetic bearings has been introduced in Chapter 6. G. Genta Torino, September 1994 Preface The current book originates from the need felt by the author to give a systematicform to the contents ofthe lectures he gives to mechani caland aeronauticalengineering students ofthe TechnicalUniversity (Politecnico) of Torino, within the frames of the courses of Princi ples and Methodologies of Mechanical Design and Construction of Aircraft Engines. Its main aim is to summarize the fundamentals of mechanics ofvibrations to give the needed theoreticalbackground to the engineer who has to deal with vibration analysis and to show a number ofdesign applications ofthe theory. Because the emphasis is mostlyon the practical aspects, the theoretical aspects are not dealt with in detail, particularly in areas in which a long and complex study would be needed. The book is structuredin six chapters. The basic concepts oflinear dynamicsofdiscretesystemsaresummarizedinChapter 1.Following the lines just described, some specialized topics, such as random vibrations, arejust touched on, more to remind the reader that they exist and to stimulate him to undertake a deeper study of these aspects than to supply detailed information. The dynamics of continuous systems is the subject of Chapter 2. As the analysis of the dynamic behaviour of continuous systems is now mostly performed using discretization techniques, the stress is laid mostly on these, particularly the finite element method, with Xli Preface the aim of supplying the users of commercial computer codes with the theoretical background needed to build adequate mathematical models and critically evaluate the results obtained from the com puter. The behaviour ofnonlinear systems is studied in Chapter 3, with the aim ofstressing the aspects ofthis subject that are ofinterest to engineersmore thanto theoreticalmechanicists. Therecent advances in all fields oftechnology often result in an increased nonlinearity of machines and structuralelements and designengineers mustincreas ingly face nonlinear problems: This chapter is meant to be ofhelp in this instance. Chapters 4 and 5 are devoted to the study of the dynamics of rotating and reciprocating machines. They are meant as specific ap plications ofthe more general topics studied before, and they intend to be more application-oriented than the previous ones. However, methods and mathematicalmodels that have not yet entered every day designpractice and are stillregarded as research topics, aredealt with herein. The last chapter constitutes an introduction to the dynamics of controlled structural systems, which are increasingly entering design practice and will unquestionably be used more often in the future. The subjects studied here are usually considered different fields of applied mechanics or mechanical design. Specialists in rotor dy namics, torsionalvibration,modalanalysis, nonlinear mechanics and controlled systems often speak different languages, and it is difficult for students to be aware ofthe unifying ideas that are at the base of all these different specialized fields. Theinconsistency ofthe symbols used in the different fields can be particularly confusing. In order to use a consistent symbolsystem throughout the book, some deviation from the common practice is unavoidable. The author believes that it is possible to explain all the aspects related tomechanicalvibrations (actuallynot onlymechanical) using a unified approach. The current book is an effort in this direction. S.1. units are used in the whole book, with few exceptions. The first exception is the measure of angles, for which in some cases the old unit degree is preferred to the S.1. unit radian, particularly where phase angles are concerned. Frequencies and angular veloci ties should be measured in rad/s. Sometimes the older units (Hz for frequencies and revolutions per minute [rpm]) are used, when the Preface xiii author feels that this makes things more intuitive or where normal engineering practice suggests it. In most formulas, at any rate, con sistent units are used. In very few cases this rule is not followed, but the reader is expressly warned in the text. For frequencies, no distinction is generally made between fre quency inHz and circularfrequency in rad/s. Although the authoris awareofthe subtle differences between the two quantities (or better, between the two different ways ofseeing the same quantity), which are subtended by the use oftwo different names, he chose to regard the two concepts as equivalent. A single symbol ().) is used for both and the symbol f is never used for a frequency in Hz. The period is then always equal to T = 271'/). because consistent units (in this case, rad/s) must be used in all formulas. A similar rule holds for angular velocities, which are always referred to with the symbol w. No different symbol is used for angular velocities in rpm, which in some texts are referred to by n. The use of ). instead of w for fre quencies is due to the need to avoid confusion between frequencies and angular velocities. In rotor dynamics, the speed at which the whirling motion takes place is regarded as a whirl frequency and not a whirl angular velocity (even if the expression whirl speed is sometimes used in opposition to spin speed), and symbols are used accordingly. It can be said that the concept of angular velocity is used only for the rotation of material objects, and the rotational speed of a vector in the Argand plane or of the deformed shape of a rotor (which does not involve actual rotation ofa materialobject) is considered a frequency. The author is grateful to colleagues and students in the Mechan ics Department of the Politecnico di Torino for their suggestions, criticism, and general exchange of ideas and, in particular, to the postgraduate students working in the dynamics field at the depart ment for reading the whole manuscript and checking most of the equations. Particular thanks are due to my wife, Franca, both for her encouragement and for doing the tedious work of revising the manuscript. G. Genta Torino, October 1992
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