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Spatial Seismic Excitations and Response Spectra

A random‐vibration‐based force‐response spectrum of a simple oscillating frame is proposed as a simplified measure of the effect of spatial seismic excitations on structures. Such a response spectrum reflects the effect of incoherent support motions on quasi‐static and dynamic response of structures. The response spectrum is formulated as a dynamic coefficient in terms of point spectral density and unlagged coherency of excitations as well as frequency‐response function of the oscillator. A concise analysis is performed in order to study joint effect of dynamic and quasi‐static excitations. The effect of two principal parameters (separation distance and apparent wave velocity) is analyzed in detail. It appears that for some values of natural frequency, separation distance, and apparent wave velocity the force spectrum is reduced and that for the others it is amplified. After some calibration, the derived response spectrum may find application in engineering practice as a partial coefficient.