Effects of modal incompleteness on quantification of mode shapes complexity in vibrating structures

Abstract

In experimental modal analysis, the mode shapes turn out to be complex due to the non-proportionality of damping in actual structures. For identification purposes, several indices have been proposed to quantify this complexity. Unfortunately, the effectiveness of the above indices is affected by the problem of data incompleteness that arises when a limited set of modal data is available, as in the case of reduced eigenvector components or in the case of band limited eigenvalues range. In contexts such as model updating, this problem makes it difficult to pair experimental versus numerical data and methods to compare the two sets of data are based on the reduction of numerical models or, conversely, on the expansion of the experimental one. However none of them reveals completely satisfactory. The present work aims to analyze the effectiveness of the above modal complexity indices. To this end, the most sensitive index found from previous studies is used in order to detect the mode shapes complexity compared to the damping non-proportionality in vibrating structures for different levels of modal incompleteness.