The paper presents the analysis of some two-degree-of-freedom nonlinear systems under random excitation using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization. The results obtained shows that the new technique can be very efficiently used not only for simple-degree-of-freedom systems as presented in the previous papers, but also for multi-degree-of-freedom ones. | Vietnam Journal of Mechanics, NCST of V ietnam Vol. 23, 200 1, No 2 (95 - 109) APPROXIMATE ANALYSIS OF SOME TWO-DEGREEOF-FREEDOM NONLINEAR RANDOM SYSTEMS BY AN EXTENSION OF GAUSSIAN EQU IVALEN T LIN EARIZATION Luu XUAN HUNG Institute of Mechanics, NCST of Vietnam A B STRACT . The paper presents the analysis of some two-degree-of-freedom nonlinear systems under random excitation using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization. The results obtained shows that the new technique can be very efficiently used not only for simple-degree-of-freedom systems as presented in the previous papers, but also for multi-degree-of-freedom ones. The solution's accuracy obtained by the proposed technique is much more improved than that using the traditional linearization. The conclusions in the paper point up the significance of this technique. 1. Introduction Gaussian equivalent linearization (GEL) proposed by Caughey [1] is presently the simplest tool widely used for analysis of nonlinear problems. However, a major limitation of this method is perhaps that its accuracy decreases as the nonlinearity increases, and for many cases it can leads to unacceptable errors. Therefore, GEL has been developed by many authors [2-9] to obtain more improved solution accuracy. N. D. Anh & M. Dipaola [8] proposed "Local Mean Square Error Criterion" (LOMSEC) which is an extension of GEL. The Authors gave initial tests based on Duffing and Vanderpol oscillators under a zero mean Gaussian white noise. Following t he initial efforts of Anh & Dipaola, L. X . Hung investigated and developed the proposed technique through analysis of a series of diverse nonlinear random systems [10-11] . The obtained results show advance of LOMSEC , especially the solution accuracy is significantly improved. However , so far the proposed technique has been just tested for nonlinear random simple-degree-of-freedom (SDOF) systems. So, the problem concerned by .
