Reply to ‘Comments on “A method of determining the regions of instability of a column by a numerical method approach”’

LETTERS TO THE EDITOR

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Finally, we wish to point out that a comprehensive treatment of the integral equation technique and its applications in structural mechanics will be published shortly [3,4]. Engineering and Technology Division Argonne National Laboratory Argonne, Illinois, U.S.A. Received 15 July 197 I

DUSAN KRAJCINOVIC

REFERENCES 1. S. Z.

H. BURNEYand L. J. JAEGER1971 Journal of Sound and Vibration 15, 75-92. A method of determining the regions of instability of a column by a numerical method approach. 2. D. KRAJCINOVIC and G. HERRMANN 1970 ZnternationalJournalfor NumericalMethods in Engineering 2,551-561. Numerical solution of the dynamic stability problems. 3. N. HAJDINand D. KRAJCINOVIC 1971 ZnternationalJournalfor Numerical Methods in Engineering (in press). Integral equation method for solution of boundary value problems of structural mechanics. I. Ordinary differential equations. 4. N. HAJDINand D. KRAJCINOVIC 1971 International Journal for Numerical Methods in Engineering (in press). Integral equation method for solution of boundary value problems of structural mechanics. II. Partial differential equations.

REPLY TO ‘COMMENTS ON “A METHOD OF DETERMINING THE REGIONS OF INSTABILITY OF A COLUMN BY A NUMERICAL METHOD APPROACH”’ The authors find very interesting the alternative and general approach of Drs Krajcinovic and Herrmann to the analysis of the dynamic stability of structures. We are well aware of the use of station functions for flutter analysis [1], but we find the writers’ application of this to parametric instability very interesting. Our own approach to the problem is based upon a finite element representation of the structural member and is clearly generically different; this element model is, of course, characterized by its simplicity and one of the attractions of the analysis is that something so simple can provide useful results. On the matter of scope of applicability, we are extending the method to the study of the parametric instability of portal frames and buildings. No difficulty is foreseen. S. Z. H. BLJRNEY

McGill University Department of Civil Engineering and Applied Mechanics Montreal 110 Quebec, Canada Received 26 October 1971

L. G.

JAEGER?

REFERENCE

1. M. RAUSCHER1949 Journal of the Aeronautical Sciences. Station functions and air density variations in flutter analysis.

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