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M ERIN ., DVNAMICS S RI S or J O Roh rt . Un1v1 1 lty oi S11 IJK Mod 1 t ti no Th ory nd Prnctic Du11110 thíl 1970 o now hra11ch of v1brnt1on engin1 ormg wa v lop d, 11compn mg the rnost powcrffJI aspect~ of both XJ 1 rl11u1111n1 r111d anllly111 nl t1 clt111q11os. 1 he re.sulting tochnology lias l rn k11own a Experimental Modal'Analysis or Modal Tcstmg. Tho t hn1 1u • 1nvolvod draw on lhe é1clvances rnode 111 drg1tal s1gnal f 1 1110 ncl in f1111te oloment mothods, and provido thc means of mb111111g tho proclucts of both into a unified tool for studyino rea l tructur il v1brntion probleins. Using modal testing tochniques, the cl h p nnd fjjpquenc1os of practical structures can be measurect urntoly, llrHI llrn results displayed iri a var iety of ways. A detailed "' th mat1cal model of a test slfucture can bo cTevised direc!'fy from .uch rnoo uronionts nnd, with this, powerf ui applications are possib/e, 111 ludmg • Corr lot1on with predictt!d models leading to correction of these r .u r, ! • rr d1ct1on ot lhe effects of modifying the test structure (perhaps to 1mprov 1ts dynamics); • An ly· is of a11 assembled structure of which the testpiece forms one omponont .. or Ewins is known as a leading a~th'ority ~ the field; he has r 1v d cm award and citation from the So~iety of Experimental M chame for his promotion and teachlng of modal analysis. The text r hl original book is now presented in a new and· ciearer font, and th opportunity has been taken to revise the notation and terminology in hn with proposed international standards. ~ RESEARCH STUOIES PRESS ll'.D, ~ l 111111011, Sornorsct, England o e )> r- ~ m cn -1 Modal Testing: Theory and Practice D. J. EWINS 620.30724 1 Ew56m 1010381126/ -~ Modal Testing: Theory and Practice MECHANJCAL ENGINEERING RESEAR('ll snmms ENGINEERING DYNAMICS SERIES Series Editor: Professor J. 8. Robcrts, University of Sussex. E11gla11d 2. Modal Testing: Theory and Practicc D.J. Ewins 4. Parametric Random Vibration R. A. lbrahim 5. Statistical Dynamics of Nonlinear and Time-Yarying Systems M. T. Dimcntbcrg 6. Stral.cgics for Structural Dynamic Modification John A. Brandon 7. Fragilily Analysis of Complex Structural Systcms F. Casciati mui L. Faravelli 8. Yibroacoustical Diagnostics for Machines and Structures M. F. Dimentberg, K. V. Frolov and A. 1. Menyailov ... . 1 Modal Testing: Theory and Practice D. J. Ewins Professor of Vibration Engineering, Imperial College of Science, Technology & Medicine, London, England ~ESEARCH STUDIES PRESS LTD. Taunton, Somerset, England JOHN WILEY & SONS INC. Ncw York · Chichester · Toronto · Bri~bane · Singapore Rl"iFAIU~ ll S l lll>IFS l'RI SS 1 11>. 2-1 Bch c<lrn: lfoa<l, lilun1u11, Somcl\C1. England l'A 1 1111 > Copyrigh1 O 19114 by Research S1ud1c\ l'rcss Lld. Reprinted wi1h atncndmcnts Jurn: 1985 Rep1intcd wi1h a111cndmenrs April 1986 Reprinted 1988. 1989, 1991 , 1992 and 1994 Reprimed January 1995: revised with 11ew notation re-set b) Abracadabra~. Milton Keyne>. England All right; reo;ervcd. No pare of 1his book may be reproduccd by any rneans , nor transmiucd. nor translated into a machinc language without the wrincn pcrmis;.ion of the publisher. Marketing and Obtribution: Amlralia mui N1•n lealmul: facaranda Wilcy Ltd. GPO Box 859, Brisbanc, Queensland 4001 . Austral ia Canada: JOHN WILFY & so~s CANADA LIMITED 22 Worces1er Road, Rexdale. Ontano. Canada L11mpe. Afrírn, Mil/d/e Easr mui J11pm1: JOl IN WILEY & SONS LIMITEI) Bnffins Lanc, Chichcster, West Susscx. England Nonh and So11rh Aml'l'im: JOHN WILfY & SONS JNC. 605 Third An:nue. Nc" Yort-.. NY 10158. USA So111h Easr Asía: JOHI'\ WILEY & SONS (SEA) PTE LTD. 37 Jalan Pcmimpin 05-04 Block B Union lndu\ trial Building. Singapore 2057 Library of Congres~ Cataloging-in-Publication Data Ewins, D. J. Modal tcsting (Mechanicnl cng inccring rcscarch srudies) (Engit1ccr- ing dynamic~ series; 2) Bibliography: p. l ncludc~ indc\ 1. Vihr;1t1on \lathcmatícal modeh. 2. Structurn l dynamic, Mathema11car modcl' 1. Title. li. Serie\. Ili. Serie;.: bn!! incering dynam1c' \cri e~; 2. TA355.E97 1984 624. 1 '76 84-9988 ISBN O 47 1 9CU72 4 (Wilcy) British Librar) Cataloguing in Publication Data E:.wí n,, D. J . Modal testing. (Mcchanical Cn!!ineering rcsearch studic, . onginecring clynamics ~cries) 1. Vibrntion Mathcmatical modcl;,. 1. Title li. Serie• 620.3'0724 QA865 ISBN O 86380O17 3 IS BN O 86380O1 7 3 (Rcscarch Studic;. Press Ltd.) ISBN O 471 990472 4 (Jolm Wilcy & Sons lnc.) Primed in Gn:at Hnta111 by SRP L1d .• F.,wtcr BAFJ f'7;=m 6,,;o 3oroJ'i ZL - V. .b TOMBO: 33""!"'7/ r:J..,-,- -.. c•IKJ D.o PROC _ --1..il.3.:it 5 '1- PRff -14. I f'f .Ls;;_ D.o\T;•, -· & / _ .f o , q 1::.._ N. cm ____ __ _ CM-00102207-3 I 1 i t Preface Modal t esting t heor y a n d pract i ce 620.30724 /Ew56m (381126/97) This book attempts to provide a reasonably detailed coverage of the t.echnology ofmodal testing. This is nota new subject although many ofthe most powerful techniques have only recently been developed and the potential ofthe method only recently recognised. Modal testing is, in effect, the process of constructing a mathematical model to describe the vibration properties of a structure based on test data, rather than a conventional theoretical analysis. As such, it has applications throughout the entire field of engineering. The subject matter in the book is presented in a particular order, and that for a particular reason. ln order to take the maximum advantage of the methods of modal t.esting, it is essential that an appropriate level of expertise be reached not only in measurement and (data) analysis methods, but also in the theoretical basis upon which the technique is founded. To this end, the readeris encouraged to make a detailed study or review of the theory in Chapter 2 before proceeding to the more practical aspects of the measurement process in Chapter 3. Even here, however, a rclatively high level of theoretical competence is expected in order to understand properly the implications and limitations of the difTerent types of measurement method - sine, random and transient excitations and the like. In Chapt.er 4 , the modal analysis methods used to process the measured data are described, ranging from the basic and relatively simple to the more advanced, computer-dependent. The analysis phase continues into Chapte r 5 where thc overall modelling process is outlined, treating difTerent leveis of complexity of the model which are appropriate to the d1fTcrent applications. Then, in Chapter 6, examples are given of some of 1 hc many uses to which the product of a modal test may be put, a list vii which will undoubtedly grow in the next few ycars. The opening chapter is rather more general, and serves both us on introduction to the tcxt and also as an Overview of the subject. As such, it provides an introduction to the rest of the work for the serious student but also presents a condensation of the whole subject for readers who wish to be apprised of the general activities and capabilities of a modal testing facility but who lack the opportunity of the extensive 'hands-on' experience which is essential for mastery of the subject. (ln the short course upon which the book is based, the Overview is intended not only for those who will attend the whole course but also for their managers who can only spare a few hours!) VIII Acknowledgements It is inevitable that many people contribute to such a work such as this and I should like to acknowledge the support and assistance I have received