Pendulum Quasi-Static Drift Effect at Suspension Point Excitation by High-Frequency Polyharmonic Multiple Frequency Vibration

The paper dwells upon the dynamic behavior of a 2d pendulum under polyharmonic vibration. The study shows that the angles between the vertical coordinate axis and the directions of the individual harmonic components effects are generally different. Relying on the well-known approach, we solved the problem in two approximations. The movement of the pendulum contains two components: the "low-frequency" component and the "high-frequency" one. As the frequencies are not multiple, the movement is essentially an aperiodic process. Hence, when deriving the basic relations, it is impossible to use an effective method of averaging the solution within a period of fast oscillations. Dividing the solution by the frequencies of oscillations, we obtained an equation describing the slow motion and an approximate formula based on it for determining the pendulum quasi-static displacement, i.e., the "drift effect". The result is generalized by taking energy dissipation into account. Findings of research show that near the quasi-static position of the pendulum, loss of stability is possible as a result of parametric resonance at the combination frequencies of the external action. The paper gives an example in which an approximate solution is compared with an exact numerical simulation and shows the results of this comparison

This work was supported by the Russian Foundation for Basic Research (RFBR grant no. 20-08-01076A)

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