A procedure to identify the modal and physical parameters of a classically damped system under seismic motions

The purpose of this paper is to discuss a methodology for determining some modal parameters (frequencies, damping ratios and seismic eigenvectors) and, under certain hypotheses, the physical matrices of a general structure with proportional damping and subjected to seismic loads. The procedure is based on a time-domain state space formulation from which the modal parameters, including the seismic eigenvectors, and the complex eigenvectors of the system can be derived also in the case of limited set of instrumentations. The conditions to normalize the eigenvectors are, then, illustrated and, nally, applied to derive the second order matrices of the system. The proposed procedure is applied to some numerical examples also in the case of noise polluted measurements and to an experimental investigation performed on a four-storey steel frame subjected to earthquake excitations. An optimization procedure to improve the prediction of the rst order modal parameters of the system is also discussed and experimentally proved.