Cross-correlation coefficients and modal combination rules for non-classically damped systems

Abstract

SUMMARYIn stochastic analysis the knowledge of cross-correlation coe$cients is required in order to combine the response of the modal Single-Degree-Of-Freedom (SDOF) oscillators for obtaining the nodal response. Moreover these coe$cients play a fundamental role in the seismic analysis of structures when the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities starting from the modal maxima. Herein a method for the evaluation of the cross-correlation coe$cients for non-classically damped systems is presented. It is de"ned in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures possess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coe$cients does not require complex quantities. Moreover a further particularization of the presented method allows a simple application of the spectrum analysis requiring only one response spectrum for an assigned damping ratio.

Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

“…The good accuracy generally observed for conventional constructions, along with its ease of use, stimulated extensions and refinements of the CQC rule, specifically tailored to structures with high‐frequency modes , poundings between adjacent buildings , spectrum‐compatible seismic inputs , viscoelastically damped buildings , modal push‐over analyses , and so on. Nevertheless, it has been recognised that the conventional CQC rule is unsuitable for analysing nonclassically damped structures, and hence, alternative techniques have been proposed . Unfortunately, the additional computational burden of these advanced methods limits their practical applications.…”