Non-Gaussianclosure techniques for stationary random vibration

The classical method of statistical linearization when applied to a non-linear oscillator excited by stationary wide-band random excitation, can be considered as a procedure in which the unknown parameters in a Gaussian distribution are evaluated by means of moment identities derived from the dynamic equation of the oscillator. A systematic extension of this procedure is the method of non-Gaussian closure in which an increasing number of moment identities are used to evaluate additional parameters in a family of non-Gaussian response distributions. The method is described and illustrated by means of examples. Attention is given to the choice of representations of non-Gaussian distributions and to techniques for generating independent moment identities directly from the differential equation of the non-linear oscillator. Some shortcomings of the method are pointed out.