Error analysis of statistical linearization with gaussian closure for large-degree-of-freedom systems

Abstract

This paper contains an analysis of the error induced by applying the method of equivalent statistical linearization (ESL) to randomly excited multi-degree-of-freedom (m.d.f.) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases. The quantity that is analyzed is the variance of the top-story displacement. The m.d.f. systems under consideration obtain their nonlinearity through cubic polynomial interstory restoring forces and the external excitation is modeled as the stationary output of a Kanai-Tajimi filter. Parameters of the filter and the m.d.f. structures, as well as the intensity of the gaussian white noise, are calibrated such that quantitative comparisons of the error between the exact solutions, estimated from Monte Carlo simulations, and the ESL solutions are possible among systems of different dimensions.