MEAN AND COVARIANCE EQUATIONS FOR BOUNDARY-VALUE-PROBLEMS

Differential equations are developed for the mean and covariance funct ions of the solution of one-dimensional boundary-value problems with w hite noise input. The equations represent an extension of the classica l mean and covariance equations used in random vibration to analyze th e response of linear systems subjected to white noise input. The diffe rences between the classical and the proposed mean and covariance equa tions are caused by the incomplete specification of the state vector a t the left end of the domain of integration and the dependence of the state vector at boundaries on the input. A statically determined and a statically indetermined beam subjected to white noise are used to ill ustrate the proposed method.