This paper presents a technique for obtaining the response of linear continuous systems with parameter uncertainties subjected to deterministic excitation. The parameter uncertainties are modeled as random fields and are assumed to be time independent. The general formulation of the method is developed for a particular class of partial differential equations with random coefficients. Random shape functions are introduced to approximate the solution in the spatial domain and in the random space. A system of linear ordinary differential equations for the unknowns of the problem is derived using the weighted residual method. The system of equations is integrated in time and the response variability is computed. Application of the new method is made to a continuum described by the one-dimensional wave equation in which the stiffness properties exhibit a spatial random variation. Validation calculations show that the results from the method agree well with those obtained by direct numerical integration.

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