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Y. Vetyukov, E. Oborin, M. Krommer, V. Eliseev:
"Transient modelling of flexible belt drive dynamics using the equations of a deformable string with discontinuities";
Mathematical and Computer Modelling of Dynamical Systems, 23 (2017), 1; 40 - 54.

Dynamics of a belt drive is analysed using a non-linear model of an extensible string at contour motion, in which the trajectories of particles of the belt are predetermined. The equations of string dynamics at the tight and slack spans are considered in a fixed domain by transforming into a spatial frame. Assuming the absence of slip of the belt on the surface of the pulleys, we arrive at a new model with a discontinuous velocity field and concentrated contact forces. Finite difference discretization allows numerical analysis of the resulting system of partial differential equations with delays. Example solution for the acceleration of a belt drive and an investigation of its frequency response depending on the velocity are presented and discussed.

Belt drive, axially moving structures, Eulerian description, partial differential equations, delay differential equations, finite differences, string dynamics

http://dx.doi.org/10.1080/13873954.2016.1232281