Seismic response of coupled systems with uncertain primary system frequencies

The seismic response of a secondary system, in addition to its dynamic properties, depends upon its interaction with the primary system. In the conventional method, seismic analyses of the primary and the secondary systems are performed separately. The mass interaction between the primary and the secondary systems is ignored as is the effect of nonclassical damping. Mass interaction and nonclassical damping can significantly affect the response of the secondary system when the two uncoupled systems have tuned or nearly tuned modes. An analysis of the coupled system accounts for these effects. Further, an uncertainty in the primary system frequencies can influence the tuning between the modes of two uncoupled systems.; In the conventional analysis method, several techniques such as “Peak Broadening” and “Peak Shifting”, are used to account for an uncertainty in the primary system frequencies. Since conventional analysis method does not consider the interaction between the primary and the secondary systems, these techniques can lead to secondary system responses that are excessively conservative. In this study, we investigate the effects of this uncertainty on the response of secondary system calculated using a coupled system analysis. In a coupled system analysis, the floor spectra are neither generated nor required and, therefore, the techniques such as Peak Broadening or Peak Shifting cannot be employed.; A computationally efficient method is developed to account for the effect of uncertainty in primary system frequencies on secondary system response in a coupled system analysis. This method is based on the observation that a significant variation in the secondary system response is caused by a variation in the frequencies of only those primary system modes that are tuned or nearly tuned to the secondary system modes. The design response spectra at the base of the primary system is used as the input and the secondary system response evaluated corresponding to 84% non-exceedance probability (NEP) while considering a ±15% variation in primary system frequencies. The proposed method is verified using simple systems in which all the modes of primary and secondary systems are known as well as systems in which high frequency secondary system modes are considered to be unknown and their effect accounted for pseudostatically. The computer program CREST is modified to incorporate the proposed method.