Extraction of normal modes and full modal damping from complex modal parameters

A procedure for extracting the structural normal modes and nondiagonal damping matrix from damped system realization parameters is presented. The procedure utilizes the state-space realization of experimental data obtained using identification algorithms such as the Eigensystem Realization Algorithm and Polyreference. This realization is first decomposed into the complex damped modes of the system and each mode is then transformed into an equivalent real-valued approximation of a second-order system. The transformation yields an approximation of the normal mode frequencies, mode shapes, and damping ratios. The procedure then develops a corrective transformation that accounts for the modal coupling implicit in nonproportional damping, thus yielding the correct structural normal modes and a nondiagonal modal damping matrix for the realization. Solutions for the corrective transformation are shown to be subject to a displacement consistency criterion. The damping identification procedure is demonstrated for both overdetermined (more sensors than modes) and underdetermined (more modes than sensors) problems using simulated data.