Endless elastic beam travelling on a moving rough surface with zones of stick and sliding

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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 misalignment between the guideways at the ends of the domain results in a stationary regime of motion, which features 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 stability of the obtained solution and provides insights regarding the characteristic time scales of establishing of subsequent zones of sliding.
Funding Information
  • Österreichische Forschungsförderungsgesellschaft (861493)

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