Asymptotic modal analysis of dynamical systems: the effect of modal cross-correlation

Asymptotic modal analysis (AMA) has been shown to be a useful approximation and valid limiting case for classical modal analysis (CMA) when the number of resonant modes in a frequency bandwidth becomes sufficiently large and the cross-correlation between resonant modes is neglected. For CMA the neglect of these cross-correlations is usually justified if the damping is small and the resonant modal frequencies are well separated. In this paper it is shown that the cross-correlations may be neglected in the AMA limit even when the damping is not small. There is a rare exception to this, i.e., when two or more identical resonant frequencies occur. But this exceptional case is easily treated by including the cross-correlations for only such modes that have the same frequencies.