Eigenvalues and Eigenvectors of Structures with Supplemental Damping Devices

The adoption of supplemental damping devices is making its way into structural codes of many countries as an acknowledged protection system against seismic action. However, in the context of the civil structures community, the analysis of eigenvalues and eigenvectors is usually done adopting undamped structural modes and/or according to classical, proportional damping schemes, due to a well-established cultural background. Unfortunately, the adoption of supplemental damping devices almost often results in: • Modal damping ratios higher than 20%; • Structural models featuring non conventional, non proportional damping schemes. As a result, a conventional structural analysis can suggest misleading conclusions about the design and the effectiveness of supplemental damping devices. The present paper shows that consolidated analytical tools of the System’s Theory for the analyses of highly damped systems can be adapted to the typical framework of the civil structures community, allowing to accurately estimate modal frequencies, modal damping ratios and modal shapes without neglecting the contribution of the dampers, even in non proportional damping schemes. The proposed methodology is applied to a numerical example so as to draw some comments on the effectiveness of this protection technique and to give a design insight to follow in the preliminary stage of the design process.