Transient Axially Symmetric Excitation of a Circular Elastic Rod in Plane Strain

Abstract

Consider a long cylindrical bar (of a homogeneous, isotropic, linearly elastic material) that is initially in static equilibrium under the action of uniform radial pressure on its cylindrical surface and axial stress as required to maintain plane strain. At zero time the radial pressure is suddenly removed, but plane-strain conditions are maintained. A finite Hankel transform solution is presented for the ensuing radial displacement and for the radial, circumferential, and axial stresses—all as functions of the radial coordinate and time. Results of computations for Poisson’s ratio equal to 0.3 are presented graphically.