Forced Oscillations of a Single Degree of Freedom System withFractional Dissipation

Authors: T. M. Atanacković, D. Ć . Dolićanin, S. Pilipović

Keywords: Fractional derivative, distributed-order fractional derivative.

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Abstract:

We study motion of a single degree of freedom mechanical system consisting of a visco-elastic rod of finite length with concentrated mass at the free end. If the deformation of the rod is approximated so that rod is considered in a state of quasi-static deformation or, equivalently, if it is assumed that the rod is light (density is equal to zero) we show that the several known oscillation equations can be derived.