(untitled) (Prima Journal of Integrated Studies, 2026)
This paper addresses the problem of analytically determining the mean-square values of displacements for a beam with elastic dissipative characteristics of the hysteresis type under random parametric excitations. The nonlinear, multi-valued functional representing the dissipative property of the beam material is accounted for in a linear form using the statistical linearization method. Using the Ito method, an analytical expression for the mean-square values of the beam displacements is derived for narrow-band and wide-band random processes.