Almost sure stability of viscoelastic structural members driven by random loads

Small stochastic oscillations of viscoelastic structural members are described by linear integro-differential equations with random coefficients. Almost sure stability of the zero solution of these equations is studied by using the Laplace transform technique under the assumption that the coefficients are stationary ergodic processes. Explicit stability conditions are developed for arbitrary relaxation kernels. These conditions are applied to the stability problem for a viscoelastic bar lying on an elastic foundation and driven by random compressive forces, and upper bounds for the intensity of the random load are calculated. The effects of material and structural parameters on the upper bounds for random forces are analyzed numerically.