#### Authors:

D. P. Acharya,Indrajit Roy,H. S. Chakraborty,#### DOI NO:

https://doi.org/10.26782/jmcms.2008.06.00006#### Keywords:

visco-elastic plate,initial stress,magnetic fluid,wave propagation,#### Abstract

*The aim of the present paper is to investigate the propagation of waves in a magneto*

*visco-elastic initially stressed electrically conducting plate of finite thickness involving time*

*rate of strain and stress of higher order. The initial stress is assumed to be of the nature of*

*hydrostatic*

*tension or compression. The normal mode analysis is used to obtain the wave*

*velocity equations for the waves propagated in the plate bounded by stress free plane*

*boundaries. The wave velocity equations in different cases, obtained in this paper may be considered as more general in the sense that the results presented by other authors may be*

*obtained as special cases in the absence of additional fields. Numerical computations are*

*carried out and the effects of higher order viscoelasticity, magnetic field and initial stress on*

*the phase velocity ratio are exhibited graphically.*

#### Refference:

1) X. Wang and H. L. Dai: Magnetothermodynamic stress and perturbation

of magnetic field vector in an orthotropic thermoelastic cylinder, Int. J. Engng. Sci, 42 (2004), 539-556.

M. A. Ezzat: Fundamental solution in generalized magneto thermoelasticity

with two relaxation times for perfect conductor cylindrical region, Int. J. Engng. Sci, 42 (2004), 1503-1519.

3) Rakshit M. and Mukhopadhyay B. : An electro-magneto-thermo-visco

elastic problem in an infinite medium with a cylindrical hole, Int. J. Engng. Sei, 43 (2005), 925-936.

4) Bakshi A., Bera R. K. and Debnath L.: A study of magneto-thermo elastic

problems with thermal relaxation and heat sources in a three-dimensional infinite rotating elastic medium, Int. J. Engng. Sci, 43 (2005), 1419-1434.

5) Roy Choudhuri S. K. : Magneto-thermo-elastic waves in an infinite

perfectly conducting solid without energy dissipation, J. Tech. Phys., 47 (2006), 63-72.

6) M. I. A. Othman and Y. Song: The effect of rotation on the reflection of

magneto-thermoelastic waves under thermoelasticity without energy dissipation, Acta Mech., 184 (2006), 189-204.

Higuchi M., Kawamura R. and Tanigawa Y.: Magneto-thermo-elastic

stresses induced by a transient magnetic field in a conducting solid circular cylinder, Int. J. Solids Struct., 44 (2007) 5316-5335.Acharya D. P. and Sengupta P. R.: Magneto-thermo-elastic waves in an

initially stressed conducting Layer, Gerlands Beitr. Geophys., 87 (1978), 229-239.

9) Das S. C., Acharya D. P. and Sengupta P. R.: Magneto visco-elastic surface

waves in stressed conducting media, Sildhani , 19 (1994), 337-346.

10) Wang J. and Slattery S. P.: Thermoelasticity without energy dissipation for initially stressed bodies, Int. J. Math. Math. Sci, 31 (2002), 329-337.

11) Othman M. I. A. and Song Y.: Reflection of plane waves from an elastic

solid half-space under hydrostatic initial stress without energy dissipation, Int. J. Solids Struct., 44 (2007), 5651-5664.

12) Sharma M. D.: Effect of initial stress on reflection at the free surface of anisotropic elastic medium, J. Earth Syst. Sci., 116 (2007), 537-551.

13) Selim M. M.: Torsional waves propagation in an initially stressed dissipative

cylinder, AppL Math. Sci. 1 (2007), 1419-1427.

14) Gupta S., Chattopadhyay A. and Kumari P. : Propagation of shear wave in anisotropic medium, Appi. Math. Sci. 1 (2007), 2699-2706.

15) Yu C. P. and Tang S. : Magneto-elastic waves in initially stress’ conductors, Z. Angew. Math. Phys., 17 (1966), 766-775.

16) De S. N. and Sengupta P. R. : Magneto-elastic waves and disturbances in initially stressed conducting media, Pure Appi. Geophys. 93 (1972), 41-54.

17) Roy Choudhuri S. K. and Banerjee M.: Magneto-viscoelastic plane waves

in rotating media in the generalized thermoelasticity II, Int. J. Math. Math. Sci, 11 (2005), 1819-1834.

18) Addy S. K. and Chakraborty N. R.: Rayleigh waves in a viscoelastic half

space under initial hydrostatic stress in presence of the temperature field, Int. J. Math. Math. Sci, 24 (2005), 3883-3894.

19) Song Y. Q., Zhang Y. C., Xu H. Y. and B. H. Lu: Magneto

thermoviscoelastic wave propagation at the interface between two micropolar viscoelastic media, Appl. Math. Compu., 176 (2006), 785-802.

20) Sharma J. N. and Othman M. I. A.: Effect of rotation on generalized

thermo viscoelastic Rayleigh-Lamb waves, Int. J. Solids Struct., 44 (2007), 4243-4255.

21) Yin-feng Z. and Zhong-min W. : Transverse vibration characteristics of axially moving viscoelastic plate, Appl. Math. Mech., 28 (2007), 209-218.

22) Rakshit M. and Mukhopadhyay B. : Visco-elastic plane waves in two

dimensions using generalized theory of thermo-elasticity, Bull. Cal. Math. Soc, 99 (2007), 279-292.

23) Voigt W. : Theortische student uberdie elasticitats verhalinisse krystalle, Abh. Ges. Wiss Goetting, 34 (1887).

24) Sengupta P. R., De N., Kar M. and Debnath L.: Rotatory vibration of

sphere of higher order viscoelastic solid, Int. J. Math. Math. Sci, 17 (1994), 799-806.

25) Othman M. I. A. : Effect of rotation on plane waves in generalized thermo

elasticity with two relaxation times, Int. J. Solids Struct., 41(2004), 2939¬2956.

26) Ezzat M. A., Othman M. I., El-Karamany A. S. : Electromagneto-

thermoelastic plane waves with thermal relaxation in a medium of perfect conductivity, J. Thermal Stresses, 24 (2001), 411-432.

27) Rayleigh F. W. : On the free vibrations of an infinite plate of homogeneous isotropic elastic material, Proc, Math. Soc.20 (1989), 225-234.

28) Lamb H. : On waves in an elastic plate, Proc. Roy. Soc. (London), 93 (1916), 114-128.

29) Eringen A. C. : On Rayleigh surface waves with small wave lengths, Applied and Engineering Sciences, 1 (1973), 11-17.

30) Acharya D. P. and Mandal Asit : Effect of rotation on Rayleigh surface

waves under the linear theory of non-local elasticity, Ind. J. Theor. Phys., 52(1) (2004).