Limitations of modal analysis of damped structures

Quite recently discrete spring-damper elements are increasingly used for the low-tuned supports of nuclear power-plant buildings and equipment (reactor building, turbine-fundaments etc.) to reduce the vibration response due to the dynamic load cases earthquake and airplane crash. Because of this development, it is to be investigated whether the usual modal analysis method is applicable within the design process or should be changed respectively replaced in special cases. The paper contributes to this discussion by demonstrating and valuing the discrepancies in the different ways for the implementation of damping. Different methods for uncoupling (energy weighting, reduction to Rayleigh-damping) are compared with the solution of the coupled equations of motion. In particular vertical vibrations of a spring-damper-supported building on foundation (including ground springs) are examined using a two-degree-of-freedom-system. The results of coupled and (by force) uncoupled methods are interpreted concerning free vibration by comparison of the damping of natural vibrations, natural frequencies and natural mode shapes. The effect on the forced vibrations is shown by floor response spectra to an earthquake accelerogram. (orig./HP)