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Research Article
Yury Vetyukov
Technische Universitat Wien
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6931-0099
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This work is licensed under a CC BY 4.0 License. Read Full License
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 into 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.
Keywords
Axially moving beam, Transport, Coulomb friction, Steady motion, Self-similarity, Transient dynamics
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CURRENT STATUS: Under Review
Version 1
Posted 09 Mar, 2021
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Received 07 Mar, 2021
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Subject Areas
Thermodynamics and statistical mechanics
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This preprint is under consideration at Nonlinear Dynamics. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research Article
Yury Vetyukov
Technische Universitat Wien
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6931-0099
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 1
Posted 09 Mar, 2021
No community comments so far
Review #? received
Received 07 Mar, 2021
Reviewers invited
Invitations sent on 04 Mar, 2021
Editor assigned
On 03 Feb, 2021
First submitted
On 03 Feb, 2021
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Thermodynamics and statistical mechanics
License:
This work is licensed under a CC BY 4.0 License. Read Full License
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 into 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.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
This preprint is available for download as a PDF.
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