Deformation of the elastic pendulum thread at resonance

DOI: 10.34759/trd-2023-130-03

Аuthors

Grishakin V. T.

Moscow Automobile and Road Construction State Technical University (MADI), MADI, 64, Leningradsky Prospect, Moscow, 125319, Russia

e-mail: grichacin@yandex.ru

Abstract

The article deals with the problems of free plane and spatial oscillations of a spring pendulum at the frequencies ratio of linear and longitudinal oscillations leading to resonance. Various mathematical models of the studied mechanical systems are adduced, and numerical results obtained when using them are compared. The author proposed a simplified model of a flat spring pendulum, which application is possible in solving engineering problems. The article illustrates the effects of the swing energy «pumping» into the axial oscillations energy of the pendulum and rotation of the pendulum material point trajectory around the vertical axis at a resonance of 1 : 1 : 2. It is established that with different frequency ratios of linear and longitudinal oscillations, the specified effect of the oscillation energy «pumping» is not observed. The effect of the swing plane rotation herewith remains, but manifests itself to a lesser extent. The trajectories of the first 20 s of the material point of the spatial spring pendulum movement at resonances were compared 1 : 1 : 2, 1 : 1 : 3 and 1 : 1 : 5. Maximum values of the thread relative deformation depending on the initial conditions of the problem under consideration are adduced for the first computational case. Computational results are summarized in a table allowing evaluating the largest relative deformations of the pendulum thread depending on the initial deviations from the equilibrium position and initial impulses, which resulted in the processes under study occurrence.

Keywords:

pendulum, resonance, thread, kinetic energy, trajectory, stresses, deformations

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