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

Alain Le Bot (1) , G Duval (1) , Philippe Klein (2) , Joël Lelong (2)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 IFSTTAR/AME/LAE - Laboratoire d'Acoustique Environnementale

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.

Mots clés: SOUND AND VIBRATION; THIN SHELLS; MOVING FORCE; ROLLING CYLINDER; TYRE-ROAD NOISE; SOUND AND VIBRATION

Domaines: Vibrations [physics.class-ph]

Alain Le Bot, G Duval, Philippe Klein, Joël Lelong. Analytical solution for bending vibration of a thin-walled cylinder rolling on a time-varying force. Royal Society Open Science, 2018, 5, pp.180639. ⟨10.1098/rsos.180639⟩. ⟨hal-01847661⟩