Magneto elastic SH-type waves in a two layered infinite plate

Problems of wave propagation in perfect magnetoelastic conductors have been studied, among others, by Knopoff [1], Dunkin and Eringen [2], Yu and Tang [3], Paria [4]. Kalishki and Rogula [5] have discussed Rayleigh waves in a semi-infinite perfect electrical conductor for a single component magnetic field. The propagation of Rayleigh-type magnetoelastic waves in a semi-infinite perfect electrical conductor has also been studied by Viktorov [6] under a two component magnetic field. In a review article by Maugin [7] a detailed study of wave motion, particularly harmonic waves in a hyperelastic nonlinear dielectrics have been made. A study of SH waves in solids as a perturbation of the boundary conditions for SH bulk waves were also made by Maugin [8]. Lee and Its [9] have considered in detail the effect of a magnetic field on the propagation of Rayleigh waves, particularly under high magnetic permeability. Chakraborty and Chattopadhyay [10] have considered the problem of magnetoelastic SH waves in a perfectly conducting half-space with an upper layer and established the fact that surface waves will exist due to the presence of a magnetic field even in those cases where ordinary Love waves do not exist. Recently Acharya and Roy [11] studied the propagation of surface waves in fibre-reinforced electrically conducting elastic solids. The presence of magnetic field was seen to modulate the Rayleigh wave velocity although no discernible effect was seen on Love waves. The problem of wave propagation in plates is analogous in many respects to wave propagation in layered spaces. In the present problem, we have considered a two-layered thick plate, both layers being perfectly conducting magnetoelastic solids, and we have shown that SH-type waves can propagate either with a velocity intermediate between the respective magnetoelastic S-wave velocities in the two layers , or with a velocity greater than both of these S-wave velocities. It is also shown that the effect of the magnetic field is to alter the group velocity if the field is unidirectional with the direction of wave propagation. Numerical results have been presented to demonstrate the effect of the field in the phase and group velocities.