A new class of flexure-free torsional vibrations of annular rods

It is shown that the system of partial differential equations governing small amplitude vibrations of an elastic ring has solutions describing motions in which the axial curve C of the ring remains rigid, but executes a rocking motion while the cross-sections undergo torsional rotations about C that vary periodically both in time and in distance along C. This type of flexure-free torsional vibration can occur both in rings that are stress-free in a circular equilibrium configuration and in rings formed by bringing together and sealing, with or without the addition of twist, the ends of rods that are stress-free when straight.