New results on the identification of normal modes from experimental complex modes

Complex modes are associated to first-order representations of structural dynamics and normal (real) modes to undamped second-order models. As normal modes are needed for comparison with undamped finite element models, their determination is a key issue. Damping introduces coupling between the normal modes so that, in general, there is no simple relation between normal and complex modes. The complex modes of a second-order model are said to be complete. It is shown that a set of complex modes is complete if it verifies a defined properness condition which is used to find complete approximations of identified complex modes. The possibility of finding a complete approximation of a set of complex modes is linked to damping properties. It is shown that the traditional assumption of proportional damping can be extended to groups of vectors and that the associated separation criterion enables the selection of groups of complex modes for which a complete approximation can be found. Go-ordinate systems used to represent the mass, damping and stiffness properties determined by the proposed approach are also discussed. An experimental application of the proposed methodology is made using six independent tests of the MIT/SERC interferometer testbed. The results clearly demonstrate applicability to real structures with high modal densities and significant non-proportional damping. (C) 1997 Academic Press Limited.