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

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. Ser. Mec. 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.

[1]  B. K. Datta.  Some observations on interactions of Rayleigh waves in an elastic solid medium with the gravity field , 1986 .

[2]  A. Abd‐Allah,et al.  On a generalized thermo-elastic problem in an infinite cylinder under initial stress , 1987 .

[3]  A. Abd-alla.  Thermal stress in a transversely isotropic circular cylinder due to an instantaneous heat source , 1995 .

[4]  S. Banerjee,et al.  Magneto-thermo-elastic interactions in an infinite viscoelastic cylinder of temperature-rate dependent material subjected to a periodic loading , 1998 .

[5]  S. M. Ahmed.  RAYLEIGH WAVES IN A THERMOELASTIC GRANULAR MEDIUM UNDER INITIAL STRESS , 2000 .

[6]  A. M. Abd-Alla,et al.  Propagation of Rayleigh waves in an elastic half-space of orthotropic material , 1999, Appl. Math. Comput..

[7]  H. L,et al.  Some Problems of Geodynamics , 1912, Nature.

[8]  A. El‐naggar,et al.  On the rotation of a non-homogeneous composite infinite cylinder of orthotropic material , 1995 .

[9]  D. C. Drucker,et al.  Mechanics of Incremental Deformation , 1965 .

[10]  S. Dey,et al.  Rayleigh waves in granular medium over an initially stressed elastic half space , 1984 .

[11]  A. Abd‐Allah,et al.  Dynamical problems of thermoelastic solids , 1986 .

[12]  D. Acharya,et al.  Surface waves in an inhomogeneous elastic medium under the influence of gravity , 1992 .

[13]  L. Rayleigh.  On Waves Propagated along the Plane Surface of an Elastic Solid , 1885 .

[14]  S. M. Ahmed,et al.  Influence of gravity on the propagation of waves in granular medium , 1999, Appl. Math. Comput..

[15]  D. Chandrasekharaiah,et al.  Thermoelastic plane waves in a transversely isotropic body , 1991 .

[16]  Y. Tsai.  Thermal Stress in a Transversely Isotropic Medium Containing a Penny-Shaped Crack , 1983 .

[17]  A. Abd-alla,et al.  Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress , 1996 .