Within the framework of vibrational mechanics, a stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point was considered and the dynamic properties of its averaged motion were studied. It is shown that, unlike the ordinary Stephenson–Kapitsa pendulum with deterministic vertical oscillations of the suspension point, both an increase and a decrease in the effective natural frequency are possible under the influence of high-frequency stochastic oscillations. A formula is derived for the amplitude of low-frequency oscillations as a function of the intensity of high-frequency stochastic oscillations and the possibility of a stochastic resonance in this system is shown. The dependence of the stochastic resonance on the mass and the damping coefficient is analyzed. It is shown that the points of the stochastic resonance lie in the plane of parameters “intensity of stochastic excitation” and “amplitude of low-frequency oscillation” on a universal curve that is independent of the mass of the pendulum. Peculiar self-oscillations in a system for which stochastic oscillations are produced by a technological load and, therefore, depend monotonically on the amplitude of low-frequency oscillations are discussed. A schematic diagram of these phenomena is proposed. The motion of the machine is described by the same equations as the stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point. A strategy of control for such a vibro-machine is proposed with the aim of maintaining it at resonance and providing an energetically efficient mode of operation.
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