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A Note on the Receptance Formulation of the Method of Displaced Frequencies and its Relation to the Collar-Jahn Procedure

Published online by Cambridge University Press:  04 July 2016

A. Simpson*
Affiliation:
Department of Aeronautical Engineering, University of Bristol

Extract

In his paper, Mahalingam describes a simple receptance approach to the displaced frequency method, and shows how (in the simple case where the added mass affects the kinetic energy of one co-ordinate only) this can be applied in the determination of corrected generalised masses. A method had been propounded previously by the present author, and this accomplished the generalised mass corrections by a procedure related to the Collar-Jahn Method for the correction of an approximate set of eigenvectors.

At first sight, the methods of refs. 1 and 2 appear very different—the first being based on dynamic flexibility relations and the second on dynamic stiffness relations. Indeed, the final forms of the equations for the corrected generalised inertias obtained from the two approaches appear radically different, and it is by no means obvious that the two methods will, in general, produce identical (or nearly identical) results.

Type
Technical notes
Copyright
Copyright © Royal Aeronautical Society 1967

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References

1.Mahalingam, S.On the Determination of the Dynamic Characteristics of a Vibrating System. Journal of the Royal Aeronautical Society, Vol 71, p 793, Nov 1967.CrossRefGoogle Scholar
2.Simpson, A.An Improved Displaced Frequency Method for the Estimation of Dynamical Characteristics of Mechanical Systems. Journal of the Royal Aeronautical Society, Vol 70, p 661, 1966.CrossRefGoogle Scholar
3.Collar, A. R.Some Notes on Jahn's Method for the Improvement of Approximate Latent Roots and Vectors of a Square Matrix. Q J Math App Mech, Vol 1, p 145, 1948.Google Scholar