Within the scope Gaussian equivalent linearization (GEL), a new mean square criterion based on Hermite polynomial error sample f13:nctions for determining the coefficients of the equivalent linearization is proposed to linearize non-linear functions of the zero mean Gaussian random process. Application to the Morison's equation for wave forces is presented that shows significant improvements over the corresponding accuracy of the classical GEL. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 2 (55-: 64) AN EQUIVALENT LINEARIZATION FOR THE DRAG FORCE IN THE MORISON'S EQUATION USING HERMITE POLYNOMIAL ERROR SAMPLE FUNCTION N. H. TRINH(*), N. D. ANH (**),D. A. CUONG (*) (*) University of Le Quy Don, Hanoi, Vietnam (**) Institute of Mechanics, Hanoi, Vietnam ABSTRACT. Within the scope Gaussian equivalent linearization (GEL), a new mean square criterion based on Hermite polynomial error sample f13:nctions for determining the coefficients of the equivalent linearization is proposed to linearize non-linear functions of the zero mean Gaussian random process. Application to the Morison's equation for wave forces is presented that shows significant improvements over the corresponding accuracy of the classical GEL. 1. Introduction There has been a large amount of the extensive investigations into the response of non-linear stochastic systems due to the fact that many excitations of engineering interest are basically random in nature. Since all real engineering systems are, more or less, non-linear, it is necessary to develop approximate techniques to determine the response statistics of non-linear systems under random excitation. One of the known approximate techniques is the Gaussian equivalent linearization (GEL) which was fist proposed by Caughey [1959] and has been developed by many authors, see . [Atalik & Utku, 1976] [Casciati & Faravelli, 1986] [Anh & Schiehlen, 1997] [Roberts & Spanos, 1990]. It has been shown that GEL is presently the simplest tool widely used for analysis of non-linear stochastic problem, however, the major limitation of this method is seemingly that it's accuracy as the non-linearity increases and it can lead to unacceptable errors in the second moments. Further, if one needs more accurate approximate solutions there is no way to obtain them using the conventional version of GEL. To obtain a series of approximate solution in this excellent technique a .
