Relationship between Fourier and response spectral ratios based on random vibration theory

摘要

In this study, an expression of relationship between RSR withrnFSR is derived based on random vibration theory. Then, systemicrnrelationships between the two spectral ratios are explored basedrnon the derived equation. Following conclusions are obtained.rn(1) The shape of RSR is nearly consistent with that of FSR.rn(2) Maximum values of FSR and RSR occur at the same period,rnand the one of FSR systematically exceeds that of RSR.rn(3) The relationship between the two spectral ratios is dependentrnon oscillator damping ratio, difference between RSR and FSRrndecreases with decreasing of the damping ratio;rn(4) The relationship between RSR with FSR is also dependent onrninput seismic motion, at period range longer than the siternfundamental period, difference between RSR with FSRrndecreases with increasing of magnitude.