Theoretical study on forced transverse oscillations of root in soil with provision for soil’s elastic and damping properties
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The topic of the paper is the theory of the forced transverse oscillations performed by the root fixed in the soil under the action of the harmonic perturbing force vectored at right angle to the root’s centreline and along the line of the translational motion performed by the lifter. On the basis of applying the Ostrogradsky-Hamilton variational principle and using the equivalent schematic model developed by the authors, the expressions have been obtained that allow to determine the amplitude of the forced transverse root body oscillations as function of the perturbing force amplitude value as well as the soil’s elastic deformation and damping coefficients. The ranges of the elastic soil deformation coefficient values, at which the resonant behaviour is observed, that is, at which the forced elastic root body oscillation amplitude value exceeds the tolerance limits, have been determined for the 10, 15 and 20 Hz frequencies of the perturbing force produced by the vibrational lifting tool. That said, the mentioned oscillation amplitude values can vary from 0.58 to 0.45 m, which is sufficient to result in the root breaking. Moreover, it has been proved that, with the increase of the perturbing force frequency, the resonant behaviour ranges shift towards the increased values of the elastic soil deformation coefficient. Therefore, such elastic soil deformation coefficient ranges should be avoided in case of the lifting tool design proposed in the paper. As regards the damping properties of the soil, it has been proved that they do not cause any resonance phenomena.