Application and extension of the stochastic linearization by Anh and Di Paola

Abstract

This study deals with the stochastic linearization technique in a new setting. First of all, the usual minimum mean-square difference requirement between the original nonlinear force and its linear counterpart is replaced by the orthogonal condition. Additionally, another recently developed idea of first replacing the nonlinear terms by higher order terms, prior to its ordinary reduction to linear ones, is super-imposed with the above condition. The results are checked on several nonlinear oscillators. In the Atalik and Utku oscillator, instead of 14% error obtained with classical linearization, the error is reduced to about 3%. In the Lutes and Sarkani oscillator the error is reduced from 22.85 to 1.23%, nearly 18-fold. In the latter case the optimal number of “regulation” steps is shown to be 2.