Normalization of complex mode shapes by truncation of alpha-polynomial

Abstract

Finite Element (F.E.) models need validating in order to reliably predict the dynamic properties of the system. One parameter that is necessary for updating the analytical models is the mode shape. The mode shapes obtained from analytical models are real-valued (normal modes), whereas the experimental mode shapes are more often than not complexvalued (complex modes). In order to be able to compare the experimental and analytical mode shapes, the former needs to be normalized. Two techniques to normalize the complex mode shapes will be discussed in this paper. The first technique is a pre-processing technique based on truncation of the ? polynomial obtained from the Unified Matrix Polynomial Approach (UMPA) model of modal parameter estimation (MPE). The proposed technique eliminated the damping and normalized the complex modal vectors, however, the undamped natural frequencies deviated from that of the actual system. The disagreement in natural frequencies is explained with the help of 2 and 4 degree of freedom (DOF) analytical models. The second normalization method proposed is a post-processing technique based on the partial fraction method of residue synthesis. The technique successfully normalized the complex modal vectors with a very good correlation with the actual (complex) mode shapes resulting in a very high modal assurance criterion (MAC) value.