Математичний метод визначення стійкості коливальних систем під дією зовнішніх віброударних навантажень

Abstract

The use of vibration technology requires an in-depth study of the physical phenomena that arise in various oscillatory systems in order to determine the optimal parameters of vibration equipment to increase the efficiency of technological processes. The action of vibration shock loads in nonlinear mechanical systems leads to the appearance of physical phenomena that can have both red and dangerous characters. The need for explanation and mathematical description of a number of peculiar physical phenomena associated with the action of vibrations on mechanical systems allows us to develop promising mathematical methods for calculating complex oscillatory systems. The aim of this study is to develop a universal mathematical method for determining the stability conditions and the equilibrium positions of oscillatory systems under the influence of an external vibro-shock load. According to the Floquet-Lyapunov theory, using the periodic Green's functions on the basis of differential equations of motion and the known optimality criteria for quasiconservative systems, we determined the positions of quasiequilibrium of vibrational systems. For an oscillating system in the form of a physical pendulum with a vibrating axis, the regions of stable equilibrium are mathematically described and the possibility of stabilizing the modes of motion of such a pendulum with impulsive vibrations of the suspension point is mathematically described.