Analysis of the vibration frequency of a vertically held tree on a vibration suspension

The article provides an analysis of the vibration frequency of a vertically held tree of different heights on a vibrating suspension, which makes it possible to determine the conditions under which a vertical tree will retain its stability. Mechanical systems in the form of mathematical and physical inverted pendulums were considered. In the calculation, with maximum idealization, the entire mass of a vertically held tree was concentrated at its center of gravity. In the calculation based on a physical pendulum, in the first case, the idealization of the tree was carried out in the form of a uniform distribution of the mass of the trunk and top of the tree along the height; in the second case, a system with a known moment of inertia of the tree when felling relative to its cut was considered. The analysis showed that the most optimal values of the oscillation frequency of trees of different heights are found in a system based on a physical pendulum with a known moment of inertia relative to the cut. For example, for trees with a height of 6 to 18 m with a maximum amplitude of oscillations of 0.4, the values of the minimum required oscillations vary from 12.2 Hz to 21.2 Hz, which is 21% less than the calculation values based on a physical pendulum in the form of a homogeneous rod or 26% less than the calculation values of the system based on a mathematical pendulum. Also, the obtained graphs of the vibration frequency show that with an amplitude of vibration starting from 0.4 m and above, the difference in the vibration frequency of trees of different heights becomes minimal, and it becomes possible to select in practice vibration drive elements for trees of different parameters.

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