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Linearization of randomly excited nonlinear systems by using local mean square error criterion

The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 22, 2000, No 2 (111 - 123) LJNEARIZATION OF RANDOMLY EXCITED NONLINEAR SYSTEMS BY USING LOCAL MEAN SQUARE ERROR CRITERION Luu XUAN HUNG Institute of Mechanics, NCST of Vietnam ABSTRACT. The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. The obtained results shows that the new technique allows to get much more accurate solutions than .t hat using Caughey Criterion. The paper leads out some new conclusions which have not been found yet by the previous researches. The new conclusions more clarify the significance of this technique. 1. Introduction One is Gaussian. equivalent lineariza of the known approximate techniques . tion (GEL) which was first proposed by Caughey [1] and has been developed by many authors (see , e.g. [4, 6-9]) . It has been shown that the Caughey method is presently the simplest tool widely used for analysis of non-linear stochastic problems. However, a major limitation of this method is' perhaps that its accurctcy decreases as the non-linearity increases, and it can lead to unacceptable errors in the second moments [3, 5, 10, 11]. Further, if one needs more accurate approximate solution, there is no way to obtain them using the conventional version of Gaussian equivalent linearization. N. D . Anh and M. Dipaola proposed "Local Mean Square Error Criterion" (LOMSEC) which is an extension of GEL. The proposed technique is t hen just applied to Duffing and Van der Pol oscillators under a zero mean Gaussian white noise to show significant improvement over the accuracy of the classical GEL [8]. The publications of Anh and Dipaola [8] as well as of the previous others however have not considered other diverse systems by using the proposed technique, their comments and conclusions are therefore limited. L. X. Hung carried out a further .