© 1959 by Oxford University Press
THE GENERATION OF TORSIONAL STRESS WAVES IN A CIRCULAR CYLINDER
(
(University of Sheffield)
Now at the Engineering Department Cambridge
)
A general solution in series form is obtained for problems in which torsional waves are generated in a bar of circular section as a result of given initial conditions, or given external stresses. The solution is in effect an extension of the PochhammerChree theory of harmonic wave propagation, and it satisfies exactly the elasticity equations and the boundary conditions. A particular problem is considered in which there is a suddenly applied torque in the form of a distributed shear force acting circumferentially on the surface of the bar. In this problem the displacements at the surface are given satisfactorily by the elementary theory at large distances along the bar, except near the wave front, where the convergence of the series is slow. The derived series for stress and velocity at the surface of the bar do not converge satisfactorily. An alternative solution in terms of waves of distortion in an infinite medium is discussed.