Cumulant-Neglect Closure Method for Nonlinear Systems Under Random Excitations

The validity of the cumulant-neglect closure method is examined by applying it to a system for which an exact solution is available. A comparison of the results indicates that the Gaussian closure technique usually leads to a mean-square versus excitation strength curve which follows the same general shape as that of the exact solution but has substantial errors in some cases. The 4th order cumulant-neglect method is found to be inapplicable and to predict erroneous behavior for systems in certain parameter ranges, including a faulty prediction of a jump in response as the excitation varies through a certain critical value. On the other hand, for systems in other ranges the 4th order cumulant-neglect closure method predicts the mean square response quite well. These two parameter ranges are delineated in the paper. The 6th order cumulant-neglect closure method is also examined, leading to similar conclusions.