THE PROBLEM OF DYNAMICS AND STABILITY OF ROD PROTECTED FROM VIBRATIONS IN RANDOM PARAMETRIC EXCITATIONS

Abstract

In this paper, the problem of dynamics and stability of nonlinear vibrations of a rod with elastic dissipative characteristic of the hysteresis type in conjunction with a liquid section dynamic absorber under the influence of random parametric excitations is considered. In this case, the system of differential equations of motion is reduced to the form of a system of Ito equations using the method of stochastic averaging. From the condition that the system of motion differential equations has a non-zero solution, the system characteristic equation is formed, the stability conditions are obtained and analyzed. The boundaries of the stability and unstability are expressed analytically, which allows to determine the average quadratic values of the vibrations of the rod protected from vibrations and to fully analyze the dynamic nature.