The purpose of this paper is to discuss a methodology for determining some modal parameters (frequencies, damping ratios, and\r\nseismic eigenvectors) and, under certain hypotheses, the physical matrices of a general structure with proportional damping and\r\nsubjected to seismic loads. The procedure is based on a time-domain state space formulation from which the modal parameters,\r\nincluding the seismic eigenvectors, and the complex eigenvectors of the system can be derived also in the case of a limited set\r\nof instrumentations. The conditions to normalize the eigenvectors are then illustrated and, finally, applied to derive the secondorder\r\nmatrices of the system. The proposed procedure is applied to some numerical examples also in the case of noise-polluted\r\nmeasurements and to an experimental investigation performed on a four-story steel frame subjected to earthquake excitations.\r\nAn optimization procedure to improve the prediction of the first-order modal parameters of the system is also discussed and\r\nexperimentally proved.
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