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

In stochastic analysis the knowledge of cross-correlation coefficients is r equired in order to combine the response of the modal Single-Degree-Of-Free dom (SDOF) oscillators for obtaining the nodal response. Moreover these coe fficients play a fundamental role in the seismic analysis of structures whe n the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities start ing from the modal maxima. Herein a method for the evaluation of the cross- correlation coefficients for non-classically damped systems is presented. I t is defined in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures p ossess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coefficients 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. Copyright (C) 1999 Joh n Wiley & Sons, Ltd.