An application of the scheme of the state space integral extension for a stochastic analysis of linear transverse vibrations for a viscoelastic beam

This paper is devoted to an application of a modification for the scheme of the state space integral extension for the study of stochastic transverse oscillations of a hinged fixed linear viscoelastic beam arising under the influence of a random axial load as well as internal and external frictions. The research technique involves the decomposition of the beam profile into a Fourier series of sines and a derivation of a system of stochastic ordinary differential equations for the expansion coefficients. On the basis of this system, equations for the first moment functions for these coefficients are constructed. We demonstrate the results of calculations based on an algorithm that implements the proposed methodology.