Random parametric nonlinear vibrations of a discrete mechanical system protected from vibration

In this work, the issue of checking the dynamics of nonlinear vibrations of a mechanical system protected from vibrations in case of random parametric excitations is considered. Using the Ito method, the analytical expressions of the mean square values of the absolute accelerations of the mechanical system and the dynamic absorber were determined. Statistical linearization method based on Davidenko's hypothesis was used to determine mean squared values. The average square value change of the random parametric vibration of the mechanical system protected against vibrations with the dynamic absorber at different values of the parameter describing the width of the vibration spectrum was analysed. It is shown that if the parameter describing the width of the vibration spectrum is taken smaller, the mean square value of the random parametric vibration of the protected object combined with the dynamic absorber will have a smaller vibration. At different values of the parameter of the hysteresis loop, the change of the mean square value of the random parametric vibration was analysed and appropriate conclusions were drawn.