A Way of Getting Scaled Mode Shapes in Output Only Modal Testing

In this paper some further work is done following the idea introduced by Parloo et all where they proposed that the scaling factor should be estimated by repeated testing introducing mass changes in different points on the structure. In this paper the approximate formula for determination of the scaling factor based on the frequency shift when introducing mass changes on the structure is derived directly from the governing equation of motion. Further the error sources are studied and a new formula introducing less approximation errors on the scaling factor is proposed. Using this new formula scaling factors can be estimated from relative large frequency shifts without introducing any approximation errors. Further it is explained how testing should be performed in order to significantly reduce approximation errors due to mode shape changes and random errors due to uncertainty on the mode shape values. It turns out that if the mass changes are well distributed over the structure, then both random errors and the approximation errors will be minimized.