Stochastic Floor Response Spectra for an Actively-Controlled Secondary System

The purpose of this paper is to propose a newly floor response spectra (FRS) in order to evaluate simply the structural response of the actively-controlled secondary system subjected to earthquake. This paper adopts a linear single-degree-of-freedom system as a main structure and an active mass damper (AMD) system as the active control technology. Also, the earthquake wave is modeled as product of a non-stationary envelope function and a stationary Gaussian random process of which power spectral density is equal to the Kanai-Tajimi spectrum. The control design is executed by using linear quadratic Gaussian control strategy against an enlarged state space system. Finally, the response amplification factor is given by the combination of the obtained statistical response values and the extreme value theory. Analytical results are compared with numerical simulations, and both show a good agreement. As a result, it seems that the validity of the proposed technique is confirmed.Copyright © 2011 by ASME