ON THE PHASE AND GROUP VELOCITY OF THERMAOELASTIC RAYLEIGH WAVES IN TRANSVERSELY ISOTROPIC MATERIALS

Abstract

Rayleigh wave speed in a heat conducting transversely isotropic material with thermal relaxation is studied. Phase and group velocity for the first four modes have been computed for aluminum alloy plate at different thermal relaxation times. It is observed that if modal phase velocity decrease with increasing frequency normally dispersive profiles, phase velocity is greater than group velocity and consequently carrier travels faster than the envelope. Thus in such cases if a phase disturbance appears at the beginning of the pulse, then it overtakes and finally it disappears in the front. Rayleigh wave speed is computed the medium and compared. It is observed that thermal relaxation time effect plays a significant role thermoelastic speed of Rayleigh waves at the low values of wave number limits

Keywords

• Rayleigh waves, dispersion, phase velocity, group velocity, transversely isotropic material

References

1. Rayleigh, J. W. S., On waves propagating along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4-11, 1887.
2. Barnett, D. M., Lothe, J., Nishioka, K. and Asaro, R., J., Elastic surface waves in anisotropic crystals: a simplified method for calculating Rayleigh velocities using dislocation theory J. Phys. F Metal Phys. 3, 1083-1096, 1973.
3. Nakamura, G. and Tanuma K., A formula for the fundamental solution of anisotropic elasticity Quart. J. Mech. Appl. Math. 50, 179-194, 1997.
4. Nkemzi, D., A new formula for the velocity of Rayleigh waves, Wave Motion 26 (1997), 205.
5. Pham, Chi . Vin. and Ogden R. W., Formulas for the Rayleigh wave speed in orthotropic elastic solids. Arch. Mech., Warszawa, 56 (3), 247-265, 2004.
6. Rahman, M. and Barber J. R., Exact expressions for the roots of the secular equation For Rayleigh waves, ASME, J. Appl. Mech. 62, 250-252, 1995.
7. Royer, D., A study of the secular equation for Rayleigh waves using the root locus method, Ultrasonics 39, 223-225, 2001.
8. Barnett, D. M. and Lothe , J., Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals J. Phys. F: Metal Phys. 4, 1974, 671-686.

9. Chadwick, P. and Smith, G. D., Foundations of the theory of surface waves in anisotropic elastic materials Adv. Appl. Mech. 17, 303-376, 1977.
10. Chandrasekharaiah, D. S., "Thermoelasticity with second sound: A review. Appl. Mech. Rev., 39, pp.355-376, 1986.
11. Lothe, J. and Barnett, D. M., On the existence of surface-wave solutions for anisotropic elastic half-spaces with free surface ,J. Appl. Phys. 47, 428-433, 1976.
12. Rehman, A., Khan, A. and Ali, A., Rayleigh waves speed in transversely isotropic material. Engng. Trans. 54 (4), 323-328, 2006.
13. Nowacki, W., Dynamic Problems of Thermoelasticity, Noordhoff International Publishing, Leyden, 1975.
14. Biot, M. A., Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 1956, 240
15. Nowinski , J. L., Theory of Thermoelasticity with Applications, Sijthoff and Noordhoff, (Alphen aan den Rijn), 1978.
16. Lord H. W. and Shulman Y., A generalized theory of thermoelasticity, J. Mech. Phys. Solids, 15, pp.299-309, 1967.
17. Green, A. and Lindsay, K. A., Thermoelasticity, J. Elasticity, 2, 1-7, 1972.
18. Dhaliwal, R. S. and Sherief, H. H., Generalized thermoelasticity for an isotropic media, Quart. J. Appl. Math., 38, pp. 1-8, 1980.
19. Chandrasekharaiah, D.S., "Hyperbolic thermoelasticity: A review of recent literature. Appl. Mech. Rev., 51, pp705 -729, 1998.
20. Verma, K. L. and Hasebe, N., On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times, J. Appl. Math., 1, pp.69-83, 2004.
21. Verma, K. L. and Hasebe, N., Wave propagation in plates of general anisotropic media in generalized thermoelasticity, Int. J. Eng. Sci., 39, pp. 1739-1763, 2001,.
22. Verma, K. L., On the thermo-mechanical coupling and dispersion of thermoelastic waves with thermal relaxations, International Journal applied and Mathematics and Statistics, 3, S05, pp.34-50, Verma, K.L., Thermoelastic waves in anisotropic plates using normal mode expansion method with thermal relaxation time, World Academy of Science, Engineering and Technology, 37, pp.573- , 2008.
23. Verma, K.L., On the wave propagation in layered plates of general anisotropic media, International Journal of Mathematical, Physical and Engineering Sciences, 2(4), pp.198-204, 2008.