A New Method for Linear Dynamical Problems in Continuum Mechanics with Random Loads.
ARMY MATERIALS AND MECHANICS RESEARCH CENTER WATERTOWN MASS
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PROBLEMS IN CONTINUUM MECHANICS ARE USUALLY FORMULATED AS INITIAL-BOUNDARY VALUE PROBLEMS IN LINEAR PARTIAL DIFFERENTIAL EQUATIONS. For problems with random forcings, the paper proposes a general, rigorous, and practical method for the determination of second-order statistics of the response. The essential feature of the method is the formulation of an initial-boundary value problem for the matrix spatial correlation which contains the mean square response as a special case. The matrix auto-correlation function is determined by another initial-boundary value problem with the spatial correlation function as the initial condition. The method is particularly useful for problems for which no other practical method is available, and it is competitive with an available method for problems solvable by both. Author