Abstract
Parametric oscillations are considered for a non-linear elastic force and non-linear parametric excitation - the presence of a non-linear expression with a periodic coefficient in the oscillation equation. The model for analysis is a rod, which is driven by an energy source - an engine of limited power, connected to the rod by means of a crank and a spring. Nonlinear differential equations of motion of the system are solved using the method of direct linearization. On the basis of this method, the equations of non-stationary, stationary mo-tions and the conditions for the stability of oscillations are derived. To obtain information about the influence of a nonlinear parametric action on the dynamics of the system, calculations were carried out. A comparison of the results obtained for linear and nonlinear parametric excitations shows a significant difference. With linear elas-tic force and linear parametric excitation, the amplitude turns to infinity. And with nonlinear parametric excitation, this does not happen. The resonance regions, the shapes of curves of amplitude and load on the energy source differ (respectively, physical effects when the source speed changes).
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