Dynamic effects in multi-mass rheonomic systems at high-frequency ripple of "forms" of oscillations

Abstract

The subject of research in the article is the degeneration of the first form with a monoharmonic change in the form factor and provided that the pulsation frequency of the "forms" of oscillations reaches the second partial frequency. The goal is to assess the possibility of degeneration of the i-th form of oscillations under various laws of change in the exciting effect and to analyze this phenomenon. The objectives of the study are to build principles for assessing the impact of high-frequency pulsations of system parameters on the free oscillations of the latter. Applied methods: description of dynamic models by differential equations; frequency analysis; formation of amplitude-frequency characteristics. The obtained results: for a dynamic model with certain indicators of the leading and driven links, it was determined that with a harmonious change in the motion function with a pulsation frequency that exceeds one, when the ratio of the damping coefficients is greater than one, the effect of degeneration of the first mode of vibration is observed, as a result of which the oscillation frequency of the driven link practically corresponds to the second form. The practical significance of the work lies in the construction of a model for the formation of frequency characteristics of a dynamic model with a high-frequency pulsation of the parameters of the latter. To identify these effects, one has to abandon the traditional ideas about the smallness of inertial components caused by the nonstationarity of vibration modes.