The normalized weighting coefficient is suggested as a piecewise linear function of the squared correlation coefficient and is defined by the least square method based on the data of Lutes-Sarkani oscillator. The application to two typical nonlinear systems subjected to random excitation shows accurate approximations when the nonlinearity varies from the weak to strong levels. | Volume 36 Number 4 4 2014 Vietnam Journal of Mechanics, VAST, Vol. 36, No. 4 (2014), pp. 307 – 320 A WEIGHTED DUAL CRITERION FOR STOCHASTIC EQUIVALENT LINEARIZATION METHOD USING PIECEWISE LINEAR FUNCTIONS N. D. Anh1,2,∗ , N. N. Linh3 of Mechanics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam 2 University of Engineering and Technology, VNU, Hanoi, Vietnam 3 Construction Technical College No. 1, Hanoi, Vietnam 1 Institute ∗ E-mail: ndanh@ Received October 24, 2014 Abstract. A weighted dual mean square criterion for stochastic equivalent linearization method is considered in which the forward and backward replacements are weighted. The normalized weighting coefficient is suggested as a piecewise linear function of the squared correlation coefficient and is defined by the least square method based on the data of Lutes-Sarkani oscillator. The application to two typical nonlinear systems subjected to random excitation shows accurate approximations when the nonlinearity varies from the weak to strong levels. Keywords: Stochastic equivalent linearization, weighted dual criterion, weighting coefficient. 1. INTRODUCTION In the study of random vibration, the stochastic equivalent linearization method proposed separately in [1,2] is one of most popular methods for analyzing nonlinear system. The development of its kernel, the classical criterion, leads to several criteria that are summarized in the papers [3, 4] and presented in the books [5–7]. It can be seen that the diverse ideas and new approaches make stochastic equivalent linearization more attractive. Recently, using the dual approach introduced in [8], a dual mean square error criterion of stochastic linearization is proposed in [9] in which dual replacements are used. Its application to investigation of approximate mean-square responses shows good results in cases of Duffing, Van der Pol oscillators but unacceptable in cases of Lutes-Sarkani oscillator with variety of nonlinearities [9]. It is .
