Abstract
The Eringen problem—that of a random vibration of a uniform beam simply supported at its ends—is generalized herewith to include the effect of a deterministic axial loading. The beam is excited by a random transverse load represented by a space- and time-wise ideal white noise. A closed-form solution is obtained for the displacement space-time correlation function at zero time lag. It is shown that as the axial load approaches the Euler buckling level, the random displacement response increases indefinitely. For axial loads below this level, the obtained expressions permit explicit evaluation of probabilistic characteristics of the response.
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