Substructuring technique: improvement by means of singular value decomposition (SVD)

There are two classical methods used for the determination of the dynamic behaviour of a coupled structure: (a) analytical modeling and (b) experimental modal analysis. However, both these methods fail to give acceptable results due to various reasons. An approach which overcomes the majority of the problems encountered, is a substructuring technique which makes use of the Frequency Response Functions (FRFs) of the substructures. Nevertheless, many studies have revealed a number of problems encountered during the realization of this technique. The present paper addresses one of them : the distortion of the final results due to numerical instabilities introduced by the use of the direct inversion of a matrix, as it is required by the mathematical formulation of the substructuring technique. Specifically, the application of a pseudoinversion by means of Singular Value Decomposition (SVD) is introduced and the resulting improvement of the results is presented.