Exact solutions to a class of structure-equipment systems

Exact solutions are presented for the mean-square responses of a class of complex structure-equipment systems under dynamic loads. The complex systems consist of an n-story building with each floor supporting a branch of an equipment system. The structure-equipment systems are precisely decomposed into n subsystems whose degrees-of-freedom are only dependent on the degrees-of-freedom in each branch equipment. These results can be used to evaluate the accuracy of existing approximate techniques, to better understand the dynamic characteristics of multituned structure-equipment systems, and to study the dynamic interaction between any two branches of the equipment system. Three illustrative examples indicate that there exists an optimum design damping of the equipment anchorage in such a complex system to suppress its vibration level. Advantage can also be taken of a nonuniform mass distribution in the equipment system to further reduce its vibration. The dynamic interaction between two branch equipment is shown to be negligible unless their frequencies are tuned to that of an activated mode of the supporting system.