A Note on the Improved Displaced Frequency Method Applied to Dynamical Systems Having a Pair of Equal Frequencies

Abstract

In applying the numerical correction method to the case where two natural frequencies of the system under test are equal, it is necessary to ensure that the matrixis diagonal in order to eliminate singularities. (In this equation δA is the displaced mass matrix; is the partitioned matrix containing the two modal columns appropriate to the equal frequencies and β is a transformation matrix (2 x 2), chosen to ensure that δαb is diagonal.)