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Advances in Acoustics and Vibration
Volume 2012, Article ID 975125, 11 pages
Research Article

A Procedure to Identify the Modal and Physical Parameters of a Classically Damped System under Seismic Motions

1Department of Structural and Geotechnical Engineering, Sapienza University of Roma, 00184 Rome, Italy
2Department of Mechanics, Structures, and Environment, University of Cassino, 03043 Cassino, Italy

Received 7 June 2011; Accepted 6 September 2011

Academic Editor: Luc Gaudiller

Copyright © 2012 M. De Angelis and M. Imbimbo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.