Vol. 9, No. 2, 2021

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Stress characterization of elastodynamics for a rotating cylinder

Józef Ignaczak

Vol. 9 (2021), No. 2, 143–151
Abstract

In the present paper, the stress characterization of elastodynamics for a rotating inhomogeneous transversely isotropic cylinder under plane strain conditions is proposed. It is assumed that the geometrical axis of the cylinder coincides with the axis of rotational symmetry of the cylinder. The cylinder rotates together with the Cartesian coordinate system xi (i = 1,2,3), in which the geometrical axis of the cylinder coincides with the x3-axis, with a uniform angular velocity Ω in such a way that the acceleration of the cylinder is a sum of three components: (i) classical acceleration, (ii) centripetal acceleration, and (iii) Coriolis acceleration. It is shown that the propagation of an elastic wave in the 3D rotating cylinder can be described by a solution to the associated 2D pure stress initial-boundary value problem. Such a reduction of the 3D problem to the 2D one is based on the theorem on an alternative representation of the displacement vector field u in terms of the stress field S. An example of a complete pure stress formulation of the traction initial-boundary value problem is presented.

Keywords
stress language of elastodynamics, rotating cylinder, classical acceleration, centripetal acceleration, Coriolis acceleration, transversely isotropic inhomogeneous elastic materials, completeness of stress formulation, natural stress traction initial-boundary value problem
Mathematical Subject Classification
Primary: 74J05
Milestones
Received: 17 September 2020
Revised: 3 December 2020
Accepted: 11 March 2021
Published: 17 April 2021

Communicated by Thomas J. Pence
Authors
Józef Ignaczak
Institute of Fundamental Technological Research
Polish Academy of Sciences
Warsaw
Poland