Modal Density Influence on Modal Complexity Quantification in Dynamic Systems

Abstract

From an engineering point of view, it is important to recognize the proportional or non-proportional nature of the damping in dynamic systems. In the first case, the mode shapes are real, whereas in the second case they are complex. Typically, the entity of non-proportional damping is estimated through appropriate indices that measure the relative weight of the imaginary part of the mode shapes. A serious problem for the practical applicability of these indices is their dependence on the accuracy of the mode shapes identification. Above all, the modal density affects the identification quality by injecting fictitious complexity in the mode shapes regardless the identification technique used. It is the purpose of the paper to contribute to evaluate the effectiveness of the non-proportionality indices in the presence of modal density. The work is based on the comparison between theoretical (exact) solutions and experimental solutions. The results show that the error is almost constant up to a certain value of the modal density beyond which it markedly diverges. The results show also that the indices share the same trend even if differently scaled. The selection of the best index is also addressed.