Rayleigh Wave in an Incompressible Fibre-Reinforced Elastic Solid Half-Space
الموضوعات :
1 - Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh - 160 011, India
الکلمات المفتاحية: Rayleigh wave, Fibre-reinforced, Incompressibility, Transverse isotropy,
ملخص المقالة :
In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function. The general solution of the equation of motion is obtained, which satisfies the required radiation condition. The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for the Rayleigh wave speed. Iteration method is used to compute the numerical values of non-dimensional speed of Rayleigh wave. The dependence of the non-dimensional wave speed on non-dimensional material parameter is illustrated graphically. Effect of transverse isotropy is observed on the Rayleigh wave speed.
[1] Anderson D.L., 1961, Elastic wave propagation in layered anisotropic media , Journal of Geophysical Research 66: 2953-2963.
[2] Belfield A. J., Rogers T. G., Spencer A.J.M., 1983, Stress in elastic plates reinforced by bres lying in concentric circles , Journal of the Mechanics and Physics of Solids 31: 25-54.
[3] Bose S.K., Mal A.K., 1974, Elastic waves in a fiber reinforced composite , Journal of the Mechanics and Physics of Solids 22: 217-229.
[4] Chadwick P., Smith G.D., 1977, Foundations of the theory of surface waves in anisotropic elastic materials, Advances in Applied Mechanics 17: 303-376.
[5] Chadwick P., 1993, Wave propagation in incompressible transversely isotropic elastic media I. Homogeneous plane waves , Proceedings of the Royal Irish Academy 93A: 231-253.
[6] Crampin S., Taylor D.B., 1971, The propagation of surface waves in anisotropic media , Geophysical Journal of the Royal Astronomical Society 25: 71-87.
[7] Destrade M., 2001, Surface waves in orthotropic incompressible materials , Acoustical Society of America 110:837-840.
[8] Destrade M., 2001, The explicit secular equation for surface acoustic waves in monoclinic elastic crystals , Acoustical Society of America 109:1398-1402.
[9] Destrade M., 2001, Surface waves in orthotropic incompressible materials , Acoustical Society of America 110: 837-840.
[10] Dowaikh M.A., Ogden R.W., 1990, On surface waves and deformations in a prestressed incompressible elastic solid , The IMA Journal of Applied Mathematics 44: 261-284.
[11] Hashin Z., Rosen W. B., 1964, The elastic moduli of bre reinforced materials , Journal of Applied Mechanics 31:223-232.
[12] Malischewsky P.G., 2000, A new formula for the velocity of Rayleigh waves Wave Motion 31: 93-96.
[13] Markham M. F.,1970, Measurement of the elastic constants of fibre composites by ultrasonics, Composites 1: 145-149.
[14] Mozhaev V.G.,1995, Some new ideas in the theory of surface acoustic waves in anisotropic media , In IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics 39:455-462.
[15] Musgrave M.J.P., 1959, The propagation of elastic waves in crystals and other anisotropic media , Reports on Progress in Physics 22:74-96.
[16] Nair S., Sotiropoulos D.A., 1999, Interfacial waves in incompressible monoclinic materials with an interlayer , Mechanics of Materials 31:225-233.
[17] Nkemzi D., 1997, A new formula for the velocity of Rayleigh waves , Wave Motion 26:199-205.
[18] Rayleigh L., 1885, On waves propagated along the plane surface of an elastic solid , Proceedings of the Royal Society of London Series A 17:4-11.
[19] Ogden R.W., Vinh P.C., 2004 , On Rayleigh waves in incompressible orthotropic elastic solids , Acoustical Society of America 115:530-533.
[20] Ogden R.W., Singh B., 2011, Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited , Journal of Mechanics of Materials and Structures 6: 453-477.
[21] Ogden R.W., Singh B., 2014, The effect of rotation and initial stress on the propagation of waves in a transversely isotropic elastic solid , Wave Motion 51: 1108-1126.
[22] Royer D., Dieulesaint E., 1984, Rayleigh wave velocity and displacement in orthorhombic, tetragonal, hexagonal and cubic crystals , Acoustical Society of America 75:1438-1444.
[23] Scott N.H., Hayes M., 1976, Small vibrations of a fibre reinforced composite , Journal of Mechanics and Applied Mathematics 29:467-486.
[24] Scott N.H., 1992, Waves in a homogeneously prestrained incompressible, almost inex- tensible, fibre-reinforced elastic material , Proceedings of the Royal Irish Academy 92 A: 9-36.
[25] Scott N.H., 1991, Small vibrations of prestrained constrained elastic materials: the idealised fibre-reinforced material , International Journal of Solids and Structures 27:1969-1980.
[26] Sengupta P. R., Nath S., 2001, Surface waves in bre reinforced anisotropic elastic media , Sadhana 26:363-370.
[27] Shams M., Ogden R.W., 2014, On Rayleigh-type surface waves in an initially stressed incompressible elastic solid , The IMA Journal of Applied Mathematics 79: 360-372.
[28] Singh S. J., 2002 , Surface waves in bre reinforced anisotropic elastic media, Sadhana 27:1-3.
[29] Singh B., Singh S.J., 2004, Reection of plane waves at the free surface of a bre reinforced elastic half-space , Sadhana 29(3):249-257.
[30] Singh B., 2007, Wave propagation in an incompressible transversely isotropic fibre reinforced elastic media , Archive of Applied Mechanics 77:253-258.
[31] Singh B., Yadav A.K., 2013, Reflection of plane waves from a free surface of a rotating fibre reinforced elastic solid half-space with magnetic field , Journal of Applied Mathematics and Mechanics 9:75-91.
[32] Stoneley R., 1963, The propagation of surface waves in an elastic medium with orthorhombic symmetry , Geophysical Journal of the Royal Astronomical Society 8:176-186.
[33] Ting T.C.T., 2002, An explicit secular equation for surface waves in an elastic material of general anisotropy , Journal of Mechanics and Applied Mathematics 55:297-311.
[34] Vinh P.C., Linh N.T.K., 2013, Rayleigh waves in an incompressible elastic half-space overlaid with a water layer under the effect of gravity, Meccanica 48:2051-2060.