Vetyukov, Y. (2021). Endless elastic beam travelling on a moving rough surface with zones of stick and sliding. Nonlinear Dynamics, 104(4), 3309–3321. https://doi.org/10.1007/s11071-021-06523-y
Electrical and Electronic Engineering; Control and Systems Engineering; Applied Mathematics; Mechanical Engineering; Aerospace Engineering; Ocean Engineering; Axially moving beam · Transport · Coulomb friction · Steady motion · Self-similarity · Transient dynamics
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Abstract:
We study the planar deformation of a beam
that travels across a given control domain supported by
a moving rough plane, which is a prototype for various
technological processes. A sufficiently small misalign-
ment between the guideways at the ends of the domain
results in a stationary regime of motion, which fea-
tures a zone of sticking contact near the entry to the
control domain, followed by infinitely many segments
of transverse sliding with alternating directions. Self-
similarity of this solution of an essentially nonlinear
boundary value problem is the primary novel result of
the present contribution. Closed-form analytic results
are validated against a finite element simulation of the
transient evolution process, which demonstrates sta-
bility of the obtained solution and provides insights
regarding the characteristic time scales of establishing
of subsequent zones of sliding.
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Project title:
Modellbildung und Simulation des lateralen Laufverhaltens von schwach gespannten Prozessstahlbändern: 861493 (FFG - Österr. Forschungsförderungs- gesellschaft mbH; Berndorf Band GmbH)
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