Finite deformations and incremental axisymmetric motions of a magnetoelastic tube

A thick-walled circular cylindrical tube made of an incompressible magnetoelastic material is subjected to a finite static deformation in the presence of an internal pressure, an axial stretch, and an azimuthal or an axial magnetic field. The dependence of the static magnetoelastic deformation on the intensity of the applied magnetic �eld is analysed for two different magnetoelastic energy density functions. Then, superimposed on this static con�guration, incremental axisymmetric motions of the tube and their dependence on the applied magnetic field and deformation parameters are studied. In particular, we show that magnetoelastic coupled waves exist only for particle motions in the azimuthal direction. For particle motion in radial and axial directions, only purely mechanical waves are able to propagate when magnetic field is absent. The wave speeds as well as the stability of the tube can be controlled by changing the internal pressure, axial stretch, and applied magnetic field that demonstrates the applicability of magneto-elastomers as wave guides and vibration absorbers