The vibration of rolling discs
The study presented is a fundamental investigation into the vibration of a rolling disc and an analysis of the sound which is then produced by the disc response. In order to characterise the disc's behaviour the free and forced vibration of a thin disc is analysed with the additional conditions which occur in rolling. These conditions include the geometric boundary conditions, the effect of the in-plane load, the change due to rotation of the disc and the effect of contact on the disc which in the first instance is modelled as a simple pinning constraint. Further in depth analysis is described for a more realistic model of the rolling contact including the effect of the contact stiffness and the creepage forces which may be present and simple contact models are proposed and corresponding responses predicted. Possible various sources of excitation are examined which cover the Rigid Body dynamics of the rolling disc, the effect of the contact model as a source of excitation and a preliminary consideration of the forces generated by contact of rough surfaces. An elementary representation is presented for the sound radiated by the rolling disc, assuming it is baffled, and its efficiency evaluated and the unbaffled disc radiation is also presented for a particular case.