This paper shows that the equivalent nonlinear equation method can be used to obtain the approximate solutions of the nonlinear rolling response of ships to non-white random excitation. The results of the proposed scheme are compared with those of the equivalent linearization method. Simulations are obtained by using summation of the random cosine series to confirm the results. The proposed equivalent nonlinear equation method is to be preferred over the equivalent linearization method.
This paper presents the results of a study Investigating a method of predicting nonlinear rolling motion of ships in irregular waves by use of an equivalent nonlinear equation(ENLE) method. In the past, an equivalent linearlzation(EL) method has been widely adopted in random vibration problems as well as ship rolling motion for nonlinear systems. (Booton,1954) (CaugheY,1963, a) (Kaplan,1966) But when the nonlinearity is strong, the high order moment statistics may not be reliable. A better approximate method known as the ENLE method has been introduced. In the study, the adopted ENLE method was capable of solving the problem of nonlinear rolling motion of a ship 10 Irregular waves with nonlinear restoring as well as nonlinear damping In the field of random vibration of the stochastic analysis has been concentrated on the calculation of response to white noise. However, in the real ocean, the excitation can not be modeled as white noise. To treat the non-white noise input Dunne(1982) has developed a new approximate method for dealing with a nonlinear systems. His method is based on the assumption that the needed statistics of the response can be approximately replaced by the excitation with a white noise process of suitable intensity. Based on this assumption, he combined the method of EL method and the FPK technique to obtain some useful results.
