Seismic Floor Response Spectra for a Combined System by Green's Functions

Keywords: Floor Response Spectra, Linear Secondary Systems, Modal Analysis, Response Approximation, and Seismic Performance.

Abstract: A parametric study of the response of a class of linear secondary systems to earthquake excitations is made. The combined dynamical system studied consists of a single-degree-of-freedom oscillator attached to a continuous cantilever beam. The generalized differential equation governing free vibration is solved exactly for the modes of the combined system. Floor response spectra for records from the 1985 Mexico City and the 1940 El Centro earthquakes are presented in several formats. The floor response spectrum concept is an extension of the widely used ground response spectrum concept and may provide useful insight into the behavior of linear secondary systems. The effects of each of the system parameters are examined. It is shown that the frequency characteristics of the excitation modify the relative importance of the system parameters. The study also demonstrates the effectiveness and limitations of the cascade approximation which is often applied as an approximate solution to the problem.