Open AccessAnalytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force
Author(s) -
Alain Le Bot,
Guillaume Duval,
Philippe Klein,
Joël Lelong
Publication year - 2018
Publication title -
royal society open science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 51
ISSN - 2054-5703
DOI - 10.1098/rsos.180639
Subject(s) - vibration , orthotropic material , cylinder , bending , mechanics , plane (geometry) , series (stratigraphy) , physics , structural engineering , classical mechanics , materials science , mathematical analysis , mathematics , acoustics , geometry , engineering , finite element method , paleontology , biology
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.