JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Generalized Rayleigh wave propagation in a covered half-space with liquid upper layer
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Generalized Rayleigh wave propagation in a covered half-space with liquid upper layer
Negin, Masoud;
 Abstract
Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.
 Keywords
generalized Rayleigh wave;initial stresses;dead forces;follower forces;wave dispersion;third order elasticity constants;
 Language
English
 Cited by
 References
1.
Akbarov, S.D. (2007), "Recent investigations on the dynamical problems of the elastic body with initial (residual) stresses (review)", Int. Appl. Mech., 43(12), 3-27.

2.
Akbarov, S.D. (2012), "The influence of third order elastic constants on axisymmetric wave propagation velocity in the two-layered pre-stressed hollow cylinder", CMC: Comput. Mater. Continua, 32(1), 29-60.

3.
Akbarov, S.D., Agasiyev, E.R. and Zamanov, A.D. (2011), "Wave propagation in a pre-strained compressible elastic sandwich plate", Eur. J. Mech. A/Solid., 30, 409-422.

4.
Akbarov, S.D. and Ipek, C. (2010), "The influence of the imperfectness of the interface conditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained compound cylinder", CMES: Comput. Model. Eng. Sci., 70(2), 93-121.

5.
Akbarov, S.D. and Ipek, C. (2012), "Dispersion of axisymmetric longitudinal waves in the pre-strained imperfectly bonded bi-layered hollow cylinder", CMC: Comput. Mater. Continua, 30(2), 99-144.

6.
Akbarov, S.D. and Negin, M. (2015), "Near-surface waves in a system consisting of a covering layer and a half-space with imperfect interface under two-axial initial stresses", J. Vib. Control, DOI: 10.1177/1077546315575466. crossref(new window)

7.
Akbarov, S.D. and Ozisik, M. (2003), "The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane", Int. J. Eng. Sci., 41, 2047-2061. crossref(new window)

8.
Biot, M.A. (1965), Mechanics of incremental deformations: Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain, John Wiley & Sons, New York, USA.

9.
Dowaikh, M.A. and Ogden, R.W. (1991), "Interfacial waves and deformations in pre-stressed elastic media", Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 433(1888), 313-328. crossref(new window)

10.
Eringen, A.C. and Suhubi, E.S. (1975a), Elastodynamics, Volume I, Finite Motions, Academic Press, New York, USA.

11.
Eringen, A.C. and Suhubi, E.S. (1975b), Elastodynamics, Volume II, Linear Theory, Academic Press, New York, USA.

12.
Gupta, S., Majhi, D.K. and Vishwakarma, S.K. (2012), "Torsional surface wave propagation in an initially stressed non-homogeneous layer over a non-homogeneous half-space", Appl. Math. Comput., 219(6), 3209-3218. crossref(new window)

13.
Guz, A.N. (1999), Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin.

14.
Guz, A.N. (2002), "Elastic waves in bodies with initial (residual) stresses", Int. Appl. Mech., 38(1), 23-59. crossref(new window)

15.
Guz, A.N. (2004), "Elastic waves in Bodies with Initial (Residual) Stresses", A.S.K, Kiev, Ukraine. (in Russian)

16.
Guz, A.N. (2005), "On foundations of the ultrasonic non-destructive method of determination of stresses in near-the-surface layers of solid bodies", CMES: Comput. Model. Eng. Sci., 8(3), 217-230.

17.
Guz, A.N. and Makhort, F.G. (2000), "Physical principles of ultrasonic non-destructive method of determination of stresses in rigid solids", Int. Appl. Mech., 36, 3-34.

18.
Negin, M., Akbarov, S.D. and Erguven, M.E. (2014), "Generalized Rayleigh wave dispersion analysis in a pre-stressed elastic stratified half-space with imperfectly bonded interfaces", CMC: Comput., Mater. Continua, 42(1), 25-61.

19.
Ogden, R. and Singh, B. (2011), "Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited", J. Mech. Mater. Struct., 6(1), 453-477. crossref(new window)

20.
Rogerson, G.A. and Fu, Y.B. (1995), "An asymptotic analysis of the dispersion relation of a pre-stressed incompressible elastic plate", Acta Mechanica, 111(1-2), 59-74. crossref(new window)

21.
Shams, M. and Ogden, R.W. (2014), "On Rayleigh-type surface waves in an initially stressed incompressible elastic solid", IMA J. Appl. Math., 79(2), 360-376. crossref(new window)

22.
Sotiropoulos, D.A. (1998), "Interfacial waves in pre-stressed compressible elastic media", Comput. Mech., 21(4-5), 293-299. crossref(new window)

23.
Tolstoy, I. and Usdin, E. (1953), "Dispersive properties of stratified elastic and liquid media: a ray theory", Geophys., 18, 844-870. crossref(new window)

24.
Wijeyewickrema, A., Ushida, Y. and Kayestha, P. (2008), "Wave propagation in a pre-stressed compressible elastic layer with constrained boundaries", J. Mech. Mater. Struct., 3(10), 1963-1976. crossref(new window)

25.
Zhang, R., Pang, Y. and Feng W. (2014), "Propagation of Rayleigh waves in a magneto-electro-elastic half-space with initial stress", Mech. Adv. Mater. Struct., 21(7), 538-543. crossref(new window)

26.
Zhang, X.M. and Yu, J.G. (2013), "Effects of initial stresses on guided waves in unidirectional plates", Arch. Mech., 65(1), 3-26.