Abstract
This paper deals with the nonlinear random response of single-degree-of-freedom systems with slip-type hysteretic restoring force characteristics, when subjected to ground motions which have the Markoffian spectra. The attention is focussed on the time change of the expected equivalent natural frequency ratio β and of the expected cumulative plastic deformation ratio λ. The approximate solutions for β and λ are derived on the basis of the theoretical investigation. They are explicitly represented in terms of two parameters - the ratio of natural frequency in the elastic range to the half-power point of Markoffian spectrum υ and the product of the nondimensional input intensity ξ and the nondimensional time τ. Both β-ξτ and λ-ξτ relations with the parameter υ reasonably reflect the nonlinearity of the hysteretic system and the property of Markoffian spectrum where the spectral density increases as the frequency decreases. In the inelastic case the value of spectral density at the initial natural frequency plays a less important role than in the elastic case. The approximate solutions are compared with the digital estimates obtained from the Monte Carlo simulation. The agreements between the both are satisfactory over the wide ranges of related parameters.
