Predicting the Dynamic Behavior of a Coupled Structure Using Frequency-Response Functions

Abstract

The mathematical formulation of the coupling method that allows the prediction of the dynamic behavior of a coupled structure by means of frequency-response functions (FRFs) of the components it consists of is well established. However, this method fails to perform in many cases. The main deficiencies are the omission of the rotational degrees of freedom, due to the difficulty in measuring FRFs for these degree of freedom, and the direct inversion of the summation matrix of the component FRFs at the coupling points, the core of the coupling method. During the investigation of these deficiencies, it was found that the lack of information about the rotational degrees of freedom lead to a negative frequency shift of the predictions. It was also proven, by means of singular value decomposition (SVD) theory, that the difficulties encountered during the direct inversion of the matrix are due to ill-conditioning effects. Additionally, a pseudoinversion was applied utilizing the SVD theory, which led to an improvement in the accuracy of the coupling procedure for the majority of the cases. Finally, for the instances where inaccuracies persisted, a new algorithm was developed and shown to improve the pseudoinversion results greatly.