Analytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force

This paper presents the analytical solution of radial vibration of a rolling cylinder submitted to a time-varying point force. In the simplest situation of simply supported edges and zero in-plane vibration, the cylinder is equivalent to an orthotropic pre-stressed plate resting on a visco-elastic f...

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Bibliographic Details
Published in:Royal Society open science 2018-07, Vol.5 (7), p.180639-180639
Main Authors: Le Bot, A., Duval, G., Klein, P., Lelong, J.
Format: Article
Language:English
Subjects:
Engineering Sciences
Mechanics
Moving Force
Physics
Rolling Cylinder
Sound And Vibration
Thin Shells
Tyre–road Noise
Vibrations
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Summary:This paper presents the analytical solution of radial vibration of a rolling cylinder submitted to a time-varying point force. In the simplest situation of simply supported edges and zero in-plane vibration, the cylinder is equivalent to an orthotropic pre-stressed plate resting on a visco-elastic foundation. We give the closed-form solution of vibration as a series of normal modes whose coefficients are explicitly calculated. Cases of both deterministic and random forces are examined. We analyse the effect of rolling speed on merging of vibrational energy induced by Doppler's effect for the example of rolling tyre.
ISSN:2054-5703
2054-5703
DOI:10.1098/rsos.180639