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 themodal parameters, including the seismic eigenvectors, and the complex eigenvectors of thesystem can be derived also in the case of a limited set of instrumentations. The conditions tonormalize the eigenvectors are then illustrated and, finally, applied to derive the second-ordermatrices of the system. The proposed procedure is applied to some numerical examples alsoin the case of noise-polluted measurements and to an experimental investigation performedon a four-story steel frame subjected to earthquake excitations. An optimization procedureto improve the prediction of the first-order modal parameters of the system is also discussedand experimentally proved