Frequency Response of Secondary Systems Under Seismic Excitation
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The main objective of this report is to investigate how the component-mode procedure can be utilized to full advantage by including the smallest number of normal modes of the primary system in the analysis while still achieving the necessary accuracy in the results. For this purpose, numerical calculations are carried out for the frequency response of a single degree of freedom secondary system supported on an arbitrary floor in a multi-story building of shear-wall type construction. It is shown that when the secondary system is tuned to one of the natural frequencies of the primary system, sufficiently accurate results can usually be obtained by including the tuned primary mode, one immediately higher than the tuned primary mode, and all of those lower than the the tuned primary mode. Therefore, the calculation is relatively simple when the secondary system is tuned to a lower primary mode; however, this computational advantage is reduced progressively as the secondary system is tuned to higher and higher primary modes. In the latter case, a modified cascade approach is found to be more efficient in which the response near the natural frequencies of some selected primary modes is calculated on the basis of the component-mode approach including these primary modes, whereas the response for the remaining frequency region is calculated using the traditional cascade procedure. The selected primary modes normally include the one in tune with the secondary system and a few lowest primary modes. When damping in the primary system is sufficiently low, including only the tuned primary mode may be sufficient.