Keywords: damping ratio, operational modal analysis, stochastic subspace identification, estimation error, inverse problem, sensitivity analysis.

The fundamental law of motion governing structural dynamics has been extensively investigated by many researchers, in particular to take into account the effect of damping on the dynamic behaviour of structures. In fact, damping strongly influences the structural response under dynamic loads but a single well established formulation to represent damping forces does not exist, yet [1]. Since a model for structural damping analogous to those for mass or stiffness determination cannot be defined, an alternative is to develop empirical expressions. Nevertheless, recent developments in seismic design of structures point out the need of accurate a-priori estimates of damping, in particular when the displacement-based design approach is adopted to prevent structural damage in the presence of moderate earthquakes. Damping in structures can be predicted by defining empirical correlations but this circumstance requires the construction of a large database of consistent damping estimates for homogeneous classes of structures, reducing, at the same time, error bounds associated with experimental values of modal damping ratios [2].

Available damping data are generally scattered due to a number of different reasons: structural and soil characteristics, the need for defining a unique damping value (the so-called equivalent viscous damping) integrating different damping mechanisms, inherent limitations of data processing methods or inaccuracies in testing procedures (low quality data, short records) [2]. Definition of protocols can reduce the influence of testing and data processing procedures on the scatter affecting damping estimates: this circumstance allows attention to be focused on the actual sources of uncertainty.

The present paper, therefore, provides a contribution towards standardization of testing and data processing procedures in order to keep error bounds in modal damping ratio estimates as low as possible.

The main issues relating to experimental estimation of damping have been reviewed in this paper. Some criteria for a reliable experimental estimation of damping values have been identified, based on simulation results reported in the literature and sensitivity analyses carried out on actual measurements. A strategy for accurate damping estimation in operational conditions by stochastic subspace identification has also been developed. Starting from the theoretical background of the method, the role played by the number of block rows on the quality of modal parameter estimates has been systematically investigated through application to a real test case. Results have pointed out how an inappropriate choice of the number of block rows leads to biased results, while its careful setting through a sensitivity analysis results in optimized estimates characterized by a low level of uncertainty.

1

J. Woodhouse, "Linear damping models for structural vibration", Journal of Sound and Vibration, 215(3), 547-569, 1998. doi:10.1006/jsvi.1998.1709

2

C. Rainieri, G. Fabbrocino, E. Cosenza, "Some remarks on experimental estimation of damping for seismic design of civil constructions", Shock and Vibration, Accepted for publication, 2010.

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