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 a limited set of instrumentations. The conditions to normalize the eigenvectors are then illustrated and, finally, 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-story steel frame subjected to earthquake excitations. An optimization procedure to improve the prediction of the first-order modal parameters of the system is also discussed and experimentally proved.