© 1968 by Oxford University Press
ON KRON'S EIGENVALUE PROCEDURE AND RELATED METHODS OF FREQUENCY ANALYSIS
(
Department of Aeronautical Engineering, University of Bristol
Department of Mechanical Engineering, University of Toronto.
)
The Kron Eigenvalue Method is discussed and developed in terms of receptances. The formulation, which is quite general, illustrates the fact that the receptance matrix of a composite system cannot be obtained directly, by standard matrix transformation alone, from the ‘primitive receptance matrix’ which comprises the receptance matrices of the subsystems into which the composite system is assumed (for the purposes of analysis) to be subdivided. However, it is shown that such transformation leads to a matrix of ‘receptance denominators’ which, when its determinant is taken and equated to zero, yields a valid frequency equation for the composite system. Kron's procedure is thereby vindicated.
A numerical (iterative) method, based on Newton's Process, for the eigenvalues of composite systems is propounded. This obviates the necessity of ‘fine-mesh frequency scanning’ when applying the Kron Method. In this respect, it is felt that the suggested procedure progresses a long way towards placing Kron's Method on a par with standard methods of numerical eigenvalue analysis.