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
(),
in which the geometrical axis of the cylinder coincides with the
-axis, with a uniform
angular velocity
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
in terms of
the stress field
.
An example of a complete pure stress formulation of the traction initial-boundary
value problem is presented.
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