1質点系RC構造物の衝撃非線形時刻歴応答の統計的変動について

Abstract

In order to obtain any response displacement x_n(t) within the nonlinear range, a new equivalent linearization method which uses repeatedly the equivalent linear-type spring modulus _<eq>k(x_n) (n=1, 2, ・・・) in terms of energy correspond to x_n(t), was devised. And by applying the perturbation method to the above method, a nonlinear random vibration method of analysis was proposed on condition that the variance of _<eq>k(x_n) which is a function of the x_n(t) is to be obtained by convergence calculations. In accordance with the proposed method, the formulations of a lumped-mass-system, where the acting loads as well as the structural properties are random variables, were endeavored and the applicability of the proposed method was examined. Futhermore, regarding a RC structure modelled trilinearly, a numerical example where almost all the structural properties are random variables, was shown. Major conclusions are summarized as follows. a) The proposed method of analysis can more accurately evaluate nonlinear random response of structures from elastic range to large deformation range, since the perturbation method and the conventional equivalent linearization method are not used in case of the linearization of the nonlinear equation of motion. b) In case that almost all the structural properties are random variables, the variance of the response dis-placement increases rapidly in the region of its maximum value. c) The proposed method can be useful means for probabilistic structural design to impulsive dynamic response, though there still remains some problems to be solved.