Effects of geometrical and loading parameters on wave propagation in a circular ring

A theoretical investigation into the transient elastic response of a circular ring under radial impact is undertaken. The effects of ring curvature, cross-section geometry and impact duration on the resulting shear force, axial force and bending moment distributions and ring deformation are examined. This extends an earlier effort (Shim, Quah, J. Appl. Mech. 65 (1998) 569–579) which employed classical Timoshenko beam theory, coupled with the method of characteristics, to analyse propagation of flexural waves in rings. The present study shows that curvature and ring cross-sectional geometry do not significantly affect the development of bending moments and shear forces but influence axial forces induced and the deformed shape. It is found that for a given impulse, propagation of generalised forces and the deformation geometry depend on impact duration. Wave speeds relating to different deformation modes are governed primarily by curvature and cross-sectional geometry.