Stability of Nonlinear Vibrations of Elastic Plate and Dynamic Absorber in Random Excitations

In this work, the problem of exploring the stability of vibrations of a hysteresis-type elastic dissipative characteristic plate with a liquid section dynamic absorber under the influence of random excitations is considered. Expressions of mean square deviations of the generalized coordinates are presented, and the expression of the spectral density of the base acceleration is obtained in the form of a wide band. The integral expressions of mean square deviations were calculated, and the conditions for the existence of vertical tangents transferred to the graph of the function representing the mean square values of displacements of plate points were determined. It is shown that these conditions are not fulfilled, and the stability condition is determined depending on the structural parameters of the system.

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