Correlation coefficients for modal response combination of non-classically damped systems Original Research Article

Correlation coefficients to perform modal combination of responses for non-classically damped systems are studied. The frequency domain analysis method is used to calculate the coefficients for 12 earthquake records and 10 damping ratios. The response of non-classically damped systems is evaluated for a range of frequencies between completely rigid and completely non-rigid. It is found that the earlier proposed linear relationship of the rigid response coefficient with frequency on a semilogarithmic graph is not accurate and that the rigid response coefficient is a function of the damping ratio. New expressions for determining the rigid response coefficients for displacement and velocity responses are proposed. The related key frequencies are also studied and found to be different from those proposed in the earlier studies. New formulations for determining these frequencies are presented. Modified equations for correlation coefficients proposed in this study are found to yield good agreement with the numerically evaluated displacement and velocity correlation coefficients for all frequency ranges. Further investigation is needed for the cross-correlation coefficient to improve the agreement with numerical results in the high frequency range.