An analysis of random linear longitudinal vibrations of a viscoelastic beam

In this paper, we present a scheme, an algorithm and results of calculations for solution of a problem about an estimation of behavior for a partial model of stochastic linear longitudinal vibrations of a viscoelastic beam for the case of difference kernel. If to use an expansion on sines of space coordinate, the form of this kernel allows to transfer the problem of analysis of stochastic integro-differential equation's system to study of stochastic differential equations for time-dependent coefficients of the expansion. The method of Monte Carlo is used to estimate the first moment functions of these coefficients.