RMS Response of Cascaded MDOF Subsystem to Multiple Support Excitation

The RMS response of a general multiple degrees of freedom (MDOF) cascaded secondary system attached at several points to a primary system is obtained using time domain random vibration formulation. The primary system is excited by ground motion at multiple support points. This in turn excites the subsystem at the attachment points. To analyze a primary system, filter parameters are chosen to represent the spectral shapes of earthquakes. The output of the filter, i.e., the time histories of RMS ground excitation at support points and their cross‐correlation, is directly prescribed. Fictitious piecewise linear strength envelopes, which represent the corresponding input of the filter, are generated accordingly before engaging the filter to the system. The time history of the RMS modal coordinates of the supporting system and their cross‐correlation are evaluated and stored as input to its subsystems. To analyze a subsystem, filter parameters are chosen to represent the spectral shapes of the modal coordinates of the supporting system, with a predominant frequency equal to the corresponding natural frequency of the primary system. Piecewise linear strength envelopes are generated as the diagonal terms to match the RMS time histories of modal coordinates and the cross‐terms to match the time histories of cross‐correlation between corresponding modal coordinates. This formulation enables one to independently analyze and design various multiply supported cascaded subsystems attached to a primary system.