Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity

Abstract

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.

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“…The set of hyperbolic partial differential ( 9) and (10) along with the initial conditions ( 13) and ( 14) and boundary conditions ( 15) and ( 16) represent a linear twopoint boundary value problems for partial differential equations which will be solved by an implicit finite difference scheme is described by Abd-Elslam et al [9]. We take the finite difference grids with spatial intervals, h in the direction R and K as the time step and use the subscripts i and n to denote the ith discrete points in the R direction and nth discrete time.…”

“…Singh [3] discussed the wave propagation in thermally conducting linear fibre-reinforced composite materials. Sharma [4] investigated the propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity. Mohajer et al [5] studied the small amplitude Rayleigh-lamb wave propagation in a finitely deformed viscoelastic dielectric elastomer layer.…”

“…Sharma [9] investigated the propagation of elastic energy in a general anisotropic medium. Sharma [10] studied the Rayleigh waves in isotropic viscoelastic solid half-space. Bayones and Hussien [11] sided the propagation of Rayleigh waves in fiber-reinforced anisotropic solid thermo-viscoelastic media under the effect of rotation.…”

On Rayleigh wave field induced by surface stresses under the effect of gravity

“…The approach in the influential work [13] assumes that gravity creates a hydrostatic initial stress, see also De and Sen-Gupta [14], extending the consideration to Rayleigh-Lamb waves subject to gravity in an elastic layer. Some of the more recent works on Rayleigh and Stoneley waves under the effect of gravity include [15][16][17][18][19] accounting for the effects of anisotropy, initial stress, vertical inhomogeneity, and magneto-elasticity.…”

Tabaka İle Örtülü Yarı Düzlemdeki Yüzey Dalgalarına Tabaka Kalınlığı ve Ön Gerilmelerin Etkisinin Tam Temas Koşulları Altında İncelenmesi

“…Ele alınan problem gerek yüzey dalgaları gerekse Rayleigh dalgaları anlamında güncelliğini korumaktadır. Bu bağlamda elastik katı, viskoelastik veya sıkıştırılamaz viskoelastik ortamlarda yüzey ve Rayleigh dalga yayılımı, ön gerilmelerin dalga yayılımına olan etkilerine dair olarak (Ashayeri ve ark., 2016;Akbarov ve Negin, 2017;Sing ve ark., 2017;Sharma, 2020) güncel bazı çalışmalar olarak verilebilir.…”