Rayleigh waves on an exponentially graded poroelastic half space. (English) Zbl 1264.74120
Summary: We consider the propagation of seismic waves in isotropic poroelastic half spaces with continuously varying elastic properties, namely with an exponentially decaying depth profile. The present paper shows that the problem leads naturally to a bicubic equation. We obtain explicit inhomogeneous plane wave solutions in an exponential evanescent form with respect to the depth of half space. Further, these solutions are used to solve the boundary value problem of a Rayleigh surface wave and the secular equation is established. The results obtained theoretically are exemplified for numerical data and represented graphically for a representative poroelastic material.
MSC:
| 74J05 | Linear waves in solid mechanics |
| 74J15 | Surface waves in solid mechanics |
| 74M25 | Micromechanics of solids |
Keywords:
Rayleigh waves; elastic materials with voids; exponentially graded half space; secular equationReferences:
| [1] | Chandrasekharaiah, D.S.: Surface waves in an elastic half-space with voids. Acta Mech. 62, 77–85 (1986) · Zbl 0602.73022 · doi:10.1007/BF01175855 |
| [2] | Chiriţă, S., Ghiba, I.D.: Strong ellipticity and progressive waves in elastic materials with voids. Proc. R. Soc. A, Math. Phys. Eng. Sci. 466, 439–458 (2010) · Zbl 1195.74012 · doi:10.1098/rspa.2009.0360 |
| [3] | Chiriţă, S., Ghiba, I.D.: Inhomogeneous plane waves in elastic materials with voids. Wave Motion 47, 333–342 (2010) · Zbl 1231.35057 · doi:10.1016/j.wavemoti.2010.01.003 |
| [4] | Christov, C.I., Jordan, P.M.: Heat conduction paradox involving second sound propagation in moving media. Phys. Rev. Lett. 94, 154301 (2005) |
| [5] | Christov, I., Jordan, P.M., Christov, C.I.: Nonlinear acoustic propagation in homentropic perfect gases: a numerical study. Phys. Lett. A 353, 273–280 (2006) · doi:10.1016/j.physleta.2005.12.101 |
| [6] | Ciarletta, M., Ieşan, D.: Non-Classical Elastic Solids. Longman Scientific and Technical, Wiley, Harlow, New York (1993) · Zbl 0790.73002 |
| [7] | Ciarletta, M., Straughan, B.: Poroacoustic acceleration waves. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 462, 3493–3499 (2006) · Zbl 1149.74345 · doi:10.1098/rspa.2006.1730 |
| [8] | Ciarletta, M., Straughan, B.: Poroacoustic acceleration waves with second sound. J. Sound Vib. 306, 725–731 (2007) · Zbl 1185.74024 · doi:10.1016/j.jsv.2007.06.015 |
| [9] | Ciarletta, M., Straughan, B., Zampoli, V.: Thermo-poroacoustic acceleration waves in elastic materials with voids without energy dissipation. Int. J. Eng. Sci. 45, 736–743 (2007) · Zbl 1213.74095 · doi:10.1016/j.ijengsci.2007.05.001 |
| [10] | Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983) · Zbl 0523.73008 · doi:10.1007/BF00041230 |
| [11] | Destrade, M.: Seismic Rayleigh waves on an exponentially graded, orthotropic half-space. Proc. R. Soc. A, Math. Phys. Eng. Sci. 463, 495–502 (2007) · Zbl 1127.86003 · doi:10.1098/rspa.2006.1774 |
| [12] | Ghiba, I.D.: Semi-inverse solution for Saint-Venant’s problem in the theory of porous elastic materials. Eur. J. Mech. A, Solids 27, 1060–1074 (2008) · Zbl 1151.74354 · doi:10.1016/j.euromechsol.2007.12.008 |
| [13] | Ghiba, I.D.: Spatial estimates concerning the harmonic vibrations in rectangular plates with voids. Arch. Mech. 60, 263–279 (2008) · Zbl 1170.74336 |
| [14] | Goodman, M.A., Cowin, S.C.: A continuum theory for granular materials. Arch. Ration. Mech. Anal. 44, 249–266 (1972) · Zbl 0243.76005 |
| [15] | Gurtin, M.E.: The linear theory of elasticity. In: Truesdell, C. (ed.) Flügge’s Handbuch der Physik, vol. VIa/2, pp. 1–295. Springer, Berlin-Heidelberg-New York (1972) |
| [16] | Ieşan, D.: A theory of thermoelastic materials with voids. Acta Mech. 60, 67–89 (1986) · Zbl 0597.73007 · doi:10.1007/BF01302942 |
| [17] | Ieşan, D.: Thermoelastic Models of Continua. Kluwer Academic, London (2004) |
| [18] | Irving, R.S.: Integers, Polynomials, and Rings. Springer, New York (2004) · Zbl 1046.00002 |
| [19] | Jordan, P.M., Christov, C.I.: A simple finite difference scheme for modelling the finite-time blow-up of acoustic acceleration waves. J. Sound Vib. 281, 1207–1216 (2005) · Zbl 1236.76039 · doi:10.1016/j.jsv.2004.03.067 |
| [20] | Jordan, P.M., Puri, P.: Growth/decay of transverse acceleration waves in nonlinear elastic media. Phys. Lett. A 341, 427–434 (2005) · Zbl 1171.74321 · doi:10.1016/j.physleta.2005.05.010 |
| [21] | Nunziato, J.W., Cowin, S.C.: A nonlinear theory of elastic materials with voids. Arch. Ration. Mech. Anal. 72, 175–201 (1979) · Zbl 0444.73018 |
| [22] | Nunziato, J.W., Kennedy, J.E., Walsh, E.K.: The behavior of one-dimensional acceleration waves in an inhomogeneous granular solid. Int. J. Eng. Sci. 16, 637–648 (1978) · Zbl 0381.73025 · doi:10.1016/0020-7225(78)90041-1 |
| [23] | Nunziato, J.W., Walsh, E.K.: On the influence of void compaction and material non-uniformity on the propagation of one-dimensional acceleration waves in granular materials. Arch. Ration. Mech. Anal. 64, 299–316 (1977) · Zbl 0366.73028 |
| [24] | Nunziato, J.W., Walsh, E.K.: Addendum ”On the influence of void compaction and material non-uniformity on the propagation of one-dimensional acceleration waves in granular materials”. Arch. Ration. Mech. Anal. 67, 395–398 (1978) · Zbl 0389.73031 |
| [25] | Ostoja-Starzewski, M., Trebicki, J.: On the growth and decay of acceleration waves in random media. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 455, 2577–2614 (1999) · Zbl 0941.74027 · doi:10.1098/rspa.1999.0418 |
| [26] | Puri, P., Cowin, S.C.: Plane waves in linear elastic materials with voids. J. Elast. 15, 167–183 (1985) · Zbl 0564.73027 · doi:10.1007/BF00041991 |
| [27] | Puri, P., Jordan, P.M.: On the propagation of plane waves in type-III thermoelastic media. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 460, 3203–3221 (2004) · Zbl 1072.74038 · doi:10.1098/rspa.2004.1341 |
| [28] | Straughan, B.: Stability and Wave Motion in Porous Media. Springer, New York (2008) · Zbl 1149.76002 |
| [29] | Ting, T.C.T.: Secular equations for Rayleigh and Stoneley waves in exponentially graded elastic materials of general anisotropy under the influence of gravity. J. Elast. 105, 331–347 (2011) · Zbl 1320.74061 · doi:10.1007/s10659-011-9314-9 |
| [30] | Ting, T.C.T.: Surface waves in an exponentially graded, general anisotropic elastic material under the influence of gravity. Wave Motion 48, 335–344 (2011) · Zbl 1283.74029 · doi:10.1016/j.wavemoti.2010.12.001 |
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