Axial Vibrations of a Stochastic Rod

Abstract The free and forced axial vibration of a rod with stochastically varying mass and stiffness properties is considered. Exact probabilistic descriptions of the response variables are shown to be obtainable for a highly idealized case. The probability distributions of the eigensolutions, Green function and input receptance function for this case are obtained. The usefulness of these results as benchmarks in the study of confidence limits of responses predicted by Statistical Energy Analysis (S.E.A.) is noted.