Correlation coefficients for structures with viscoelastic dampers

The correlation coefficients of SDoF oscillators play a fundamental role in the seismic analysis of structures. These coefficients, in fact, are required in order to properly combine the modal maxima in the Lagrangian space, for example via the complete quadratic combination (CQC) rule. In the framework of the random vibration of linear systems, alternative frequency- and time-domain approaches to evaluate the correlation coefficients of SDoF oscillators with viscoelastic memory are presented, and validated by means of Monte Carlo simulation. In contrast to the usual modal strain energy (MSE) method, the proposed formulations allow the seismic analysis of structures with added viscoelastic dampers to be performed in a consistent modal space, where the fading memory arising from these devices is not neglected. Moreover, the frequency content of the ground motion can be accounted for. The numerical applications show that the inaccuracy associated with the conventional analyses (MSE+CQC) may be unacceptable for engineering purposes.