Scaling factor estimation by the mass change method

Abstract

When natural input modal analysis is performed, the acting forces are unknown; by this reason only un-scaled mode shapes may be obtained so that the FRF matrix can not be constructed. If the structure is modified and a new modal testing is carried out, the scaling factors can be determined using the modal parameters (natural frequencies and mode shapes) from both the modified and the unmodified structure. Mass change is in many cases the simplest way to perform structural modification, which involves repeated testing implying mass change in different points of the structure where the mode shapes are known. In this paper, several methods to estimate the scaling factors, based on the mass change method, are presented. The accuracy obtained through the methods proposed depends on the type of normalization used in the mode shapes, the mass change magnitude and the number and the location of the masses attached to the structure, which effect is also analyzed. Finally, it is shown how the scaling factors can be used to improve the modal updating procedures