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

Abstract

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.