Longitudinal vibrations of viscoelastic longitudinally nonuniform rod under power load distributed along its length

Gera B., Sitarz M., Bolzhelarskyi Ya.
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In this article, the dynamic behavior of a moving elongated object is simulated using the relations for a viscoelastic rod, which moves at a constant speed under the action of traction force and distributed along its length external forces of resistance. We investigate the change of displacements and internal forces after the sudden application in the rod section of the local force directed longitudinally. The correlations of the initial boundary value problem that describes the dynamic behavior of the rod are written down, and its solution is obtained in the form of a series expansion in terms of eigenfunctions. For a viscoelastic rod consisting of three connected uniform rods, the analysis of wave processes induced by the application to the rod of a sudden concentrated force that resists the motion is carried out. This affects the motion of the rod as a whole, and induces the wave processes, the propagation and reflection of waves on the inner surfaces of joints. The comparison is performed for the behavior of an elastic, piecewise nonuniform rod and a viscoelastic rod with different mechanical characteristics, where the waves during their propagation are damped and smoothed.
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Math. Model. Comput. Vol.3, No.2, pp.135-145 (2016)