Seismic analysis of coupled primary-secondary systems gives responses that are more accurate that the uncoupled analysis (Gupta 1992). A coupled analysis accounts for the mass interaction between uncoupled systems and the correlation between inputs at various supports of a multiply connected secondary system. It eliminates the need for a separate static analysis of the secondary system to account for the effect of relative support motion. Different damping characteristics of the individual classically damped primary and secondary systems make the coupled system nonclassically damped. In conventional seismic analysis, the nonclassical nature of the coupled damping matrix is not considered (off-diagonal terms in the transformed damping matrix are ignored). Ignoring the nonclassical nature of damping matrix can lead to incorrect results shwn the uncoupled primary and secondary systems are tuned or nearly tuned. A formulation is presented to calculate the damping matrix of a nonclassically damped coupled system when the individual uncoupled systems are classically damped. Significance of nonclassical damping on the secondary system response is illustrated by performing two different time history analyses of the coupled systems, one by including the offdiagonal terms in the transformed damping matrix and the other by ignoring them.
展开▼
