Plane waves in a transversely isotropic rotating magnetothermoelastic medium

Abstract

Formulation of the Problem and Its Solution. We consider an infinite, homogeneous, transversely isotropic, thermally and electrically conducting elastic medium with the reference temperature T0 under the action of a primary magnetic field with the magnetic induction B0. The medium is uniformly rotating with an angular velocity = Ωn, where n is the unit vector in the direction of the axis of rotation. The displacement equation in a rotating frame of reference includes two additional terms corresponding to the centripetal acceleration due to only time-varying motion ( × × u) and to the Coriolis acceleration ⎛ ⎝ ⎞ ⎠ a way that the planes of isotropy are perpendicular to the z axis. The origin of the frame is located on the plane surface, and the z axis is directed normally into the medium which is thus represented by z ≥ 0. We restrict our analysis to the plane strain parallel to the xz plane with the displacement vector u = (u, 0, w) and temperature T(x, z, t). We also assume that the half-space is rotating about the y axis with the angular velocity = (0, Ω, 0). We consider the time-dependent dynamic solutions and the time-independent part of the centripetal acceleration, and all the body forces are neglected, except for the time-dependent part of the electromagnetic body force. Then, the displacement equations in an elastic solid with increase in the temperature T above the reference temperature T0 are