Plane Wave Propagation Through a Planer Slab

Subject Areas : Engineering

R Kakar ¹

1 - Principal, DIPS Polytechnic College, Hoshiarpur

Received: 2012-12-08 Accepted : 2013-01-25 Published : 2013-03-30

Keywords: Plane waves, Inhomogeneous media, time-independent methods, Navier’s equations,

Abstract :

An approximation technique is considered for computing transmission and reflection coefficients for propagation of an elastic pulse through a planar slab of finite width. The propagation of elastic pulse through a planar slab is derived from first principles using straightforward time-dependent method. The paper ends with calculations of enhancement factor for the elastic plane wave and it is shown that it depends on the velocity ratio of the wave in two different media but not the incident wave form. The result, valid for quite arbitrary incident pulses and quite arbitrary slab inhomogeneities, agrees with that obtained by time-independent methods, but uses more elementary methods.

References:

[1] Poisson S. D., 1829, Memoire sur I’equilibre et le movement des corps e’lastiques, Mem de I’Acad Roy des Science I’Inst 8: 357-570.

[2] Kelvin L., 1863, On the rigidity of the earth, Philosophical Transactions of the Royal Society A 153: 573-582.

[3] Rayleigh L., 1877, On progressive waves, Proceedings of the London Mathematical Society 1-9: 21-26.

[4] Rayleigh L., 1885, On waves propagation on the plane surface of an elastic solid, Proceedings of the London Mathematical Society 17: 4-11.

[5] Rayleigh L., 1912, On the propagation of waves through a stratified medium with special reference to the question of reflection, Proceedings of the Royal Society A 86 (586): 207-226.

[6] Stoneley R., 1924, Elastic waves at the surface of separation of two solids, Proceedings of the Royal Society A 106(738): 416-428.

[7] Spencer A. J. M., 1974, Boundary layers in highly anisotropic plane elasticity, International Journal of Solids and Structures 10(10): 1103-1123.

[8] Biot M. A., 1965, Mechanics of Incremental Deformations, Wiley, New York.

[9] Love A.E.H., 1944, Mathematical Theory of Elasticity, Dover Publications, 4th edition.

[10] Epstien P.S., 1930, Reflection of waves in an inhomogeneous absorbing medium, Proceedings of the National Academy of Sciences 16: 627-637.

[11] Sinha S.B., 1999, Transmission of elastic waves through a homogenous layer sandwiched in homogenous media, Journal of Physics of the Earth 12: 1-4.

[12] Tooly R.D., Spencer T.W., Sagoci H.F., 1965, Reflection and Transmission of plane compressional waves, Geophysics 30: 552-570.

[13] Gupta RN., 1966, Reflection of elastic waves from a linear transition layer, Bulletin of the Seismological Society of America 56: 511-526.

[14] Agemi R., 2000, Global existence of nonlinear elastic waves, Inventiones mathematicae 142: 225-250.

[15] Kakar R., Kakar S., 2012, Propagation of Love waves in a non-homogeneous elastic media,Journal of Academia and Industrial Research 1(6): 323-328.

[16] Sokolnikoff I. S., 1956, Mathematical Theory of Elasticty, McGraw-Hill, New York.