The dynamic stability problem of a Timoshenko beam supported by a generalized
Pasternak-type viscoelastic foundation subjected to compressive axial
loading, where rotary inertia is neglected, is investigated. Each axial
force consists of a constant part and a time-dependent stochastic function.
By using the direct Liapunov method, bounds of the almost sure asymptotic
stability of a beam as a function of viscous damping coefficient, variance
of the stochastic force, shear correction factor, parameters of Pasternak
foundation, and intensity of the deterministic component of axial loading
are obtained. With the aim of justifying the use of the direct Liapunov
method analytical results are firstly compared with numerically obtained
results using Monte Carlo simulation method. Numerical calculations are
further performed for the Gaussian process with a zero mean as well as a
harmonic process with random phase. The main purpose of the paper is to
point at significance damping parameter of foundation on dynamic stability
of the structure.