Rayleigh waves in a magnetoelastic half-space of orthotropic material under influence of initial stress and gravity field

Abstract

In this paper, the frequency equation which determines the velocity of Rayleigh waves, including initial stress, gravity field and magnetic field, in a homogeneous orthotropic elastic medium has been obtained. The theory of generalized surface waves has firstly been developed and then it has been employed to investigate particular cases of waves, viz. Rayleigh waves under the influence of gravity field, initial stress and magnetic field. The frequency equation obtained is in agreement with the corresponding result obtained by Datta [Rev. Roumaine Sci. Tech. Sér. Méc. Appl. 31 (1986) 369], when the initial stress and magnetic field are neglected. Moreover, when the magnetic field is neglected, our result is in agreement with the corresponding result of Abd-Alla [Appl. Math. Comput. 99 (1999) 61]. Numerical results analyzing the frequency equation are discussed and presented graphically. The results indicate that the effect of orthotropy on such waves is small and can be neglected, while the effect of initial stress, magnetic field and gravity field are very pronounced.