Structure-borne sound power analysis for quantifying arbitrary structural modifications

A scalar quantity referred to as the Modification Power (MP) is presented as a means of characterizing a structure's response to modifications. The structural modifications are modeled as a perturbation of arbitrary rank to the impedance matrix describing the unmodified structure's dynamics. Perturbed matrix inversion methods are utilized to develop the MP. It is shown that this method of calculating the inverse of the modified impedance matrix is better numerically conditioned when compared to using a direct inversion method. The MP provides the analyst with information regarding not only the magnitude of the change in power flow, but the direction as well, indicating an increase or decrease in power flow into a structure. Additionally, expressions for the original and modified impedance matrices are derived in physical coordinates and reduced modal coordinates using primal assembly methods from the field of dynamic substructuring. Two case studies are presented, one using a pinned beam structure and the other a cantilevered plate structure, to demonstrate the properties of the MP, as well as to show the improved numerical conditioning of the modified impedance matrices.