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Y. Vetyukov:
"Endless elastic beam travelling on a moving rough surface with zones of stick and sliding";
Nonlinear Dynamics, 104 (2021), 3309 - 3321.

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.

Axially moving beam · Transport · Coulomb friction · Steady motion · Self-similarity · Transient dynamics

http://dx.doi.org/10.1007/s11071-021-06523-y

https://doi.org/10.1007/s11071-021-06523-y

Project Head Yury Vetyukov:
LaLaBand