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The final purpose of this paper is to estimate the efficiency of some 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, one paper by author has been derived as for the stochastic floor response spectra in consideration of a simple nonlinear design. As a second step, the multi supported secondary system is testified in consideration of correlation between multi components of input. 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, finally the stochastic dynamic characteristics of the multi-supported nonlinear system can be derived analytically. The obtained results are compared with those by Monte Carlo simulation.

Stochastic Analysis of Two-Degree-of-Freedom Structure with Elasto-Plastic Characteristics Subjected to Correlated Multiple Excitations