２次系の非弾性を考慮した確率論的床応答スペクトル

抄録

The purpose of this paper is to propose one analytical method to make stochastic floor response spectra in order to easily estimate the dynamic characteristics of secondary system such as piping, equipment and so on, mounted on a structure owing to an earthquake. Because of the increase of uncertainty at earthquake level, the design level for earthquake is tending upward. This is implying that the aseismic design of secondary system based on elastic design becomes more difficult from the viewpoint of economic design. Thus, as a first step, this paper derives the stochastic floor response spectra in consideration of a simple nonlinear design and/or a seismic risk analysis in future. The nonlinear properties of the secondary system are modeled in terms of an equation of motion which linearly involves the auxiliary variable as part of the restoring force and the auxiliary equation which describes a nonlinear relationship. Total equations including the auxiliary equation are linearized using a stochastic linearization technique. Then executing the statistical calculation to obtain the non-stationary variance relating to relative displacement of secondary system and utilizing a proposed idea to estimate the extreme value, finally the stochastic floor response spectra can be derived. The analytical results are compared with those by Monte Carlo simulation.