A Correlation Analysis of the Dynamics of a Nonlinear Model of a Structure Under Nonstationary Stochastic Loads by the Method of Moments

A generalization of the method of moments to analyze the reaction of a linearized model of a structure to arbitrary additive stochastic forcing is proposed. This generalization does not require reducing the initial system of equations in the Cauchy form to a canonical form according to which all external forces are considered as white noise. Thus, there is no need to use forming filters and therefore, there are no limitations on the nature of external loads, including stationarity. The known equations of the method of moments with regard to the mean vector and the matrix of correlation moments of the vector of phase coordinates, true only for the canonical form of the initial equation of movement, become a special case. The fundamental matrix of statistically linearized system is treated as a multiplicative integral, thus making it possible to build a simple algorithm, convenient for numerical calculation and based on recurrent formulae. The results are illustrated by an example.

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