Three-Dimensional Problems of Harmonic Wave Propagation in an Elastic Layer

Belubekyan, M.V.; Belubekyan, V.M.

doi:10.1007/978-3-030-17470-5_9

Cited by 2 publications

(8 citation statements)

References 4 publications

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“…As in problems of plane strain, the potentials

φ (x, y, z, t)

and

ψ (x, y, z, t)

are introduced according to

u = \frac{\partial φ}{\partial x} - \frac{\partial ψ}{\partial z}, w = \frac{\partial φ}{\partial z} + \frac{\partial ψ}{\partial x} .

…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Taking into account the decay conditions

\underset{y \to \infty}{trueprefixlim} \vec{u} = 0, \underset{y \to \infty}{trueprefixlim} φ = 0, \underset{y \to \infty}{trueprefixlim} ψ = 0,

for the functions

u, v, w, φ

and ψ we obtain the following representations:

u (x, y, z, t) = - i [A k prefixcos γ e^{- υ_{1} k y} + (() B k cos γ + C k sin γ) e^{- υ_{2} k y}] exp i (ω t - x k prefixcos γ - z k prefixsin γ),

v (x, y, z, t) = - k [A υ_{1} e^{- υ_{1} k y} + B {υ^{- 1}}_{2} e^{- υ_{2} k y}] exp i (ω t - x k prefixcos γ - z k prefixsin γ),

w (x, y, z, t) = - i [A k prefixsin γ e^{- υ_{1} k y} + (() B k sin γ - C k cos γ) e^{-}]

…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Periodic wave propagation in an elastic layer is studied in [12,13]. As in problems of plane strain, [5] the potentials ( , , , ) and ( , , , ) are introduced according to…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Further, substituting (2.7) into (2.8), after some transformations, we arrive at for the functions , , , and we obtain the following representations: [5] ( , , , ) = − [ cos − 1 + ( cos + sin ) − 2 ] exp ( − cos − sin ) ,…”

Section: Statement Of the Problemmentioning

confidence: 99%

See 3 more Smart Citations

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

Belubekyan¹,

Sarkisyan²

2018

Z Angew Math Mech

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show abstract

“…As in problems of plane strain, the potentials

φ (x, y, z, t)

and

ψ (x, y, z, t)

are introduced according to

u = \frac{\partial φ}{\partial x} - \frac{\partial ψ}{\partial z}, w = \frac{\partial φ}{\partial z} + \frac{\partial ψ}{\partial x} .

…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Taking into account the decay conditions

\underset{y \to \infty}{trueprefixlim} \vec{u} = 0, \underset{y \to \infty}{trueprefixlim} φ = 0, \underset{y \to \infty}{trueprefixlim} ψ = 0,

for the functions

u, v, w, φ

and ψ we obtain the following representations:

u (x, y, z, t) = - i [A k prefixcos γ e^{- υ_{1} k y} + (() B k cos γ + C k sin γ) e^{- υ_{2} k y}] exp i (ω t - x k prefixcos γ - z k prefixsin γ),

v (x, y, z, t) = - k [A υ_{1} e^{- υ_{1} k y} + B {υ^{- 1}}_{2} e^{- υ_{2} k y}] exp i (ω t - x k prefixcos γ - z k prefixsin γ),

w (x, y, z, t) = - i [A k prefixsin γ e^{- υ_{1} k y} + (() B k sin γ - C k cos γ) e^{-}]

…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…Periodic wave propagation in an elastic layer is studied in [12,13]. As in problems of plane strain, [5] the potentials ( , , , ) and ( , , , ) are introduced according to…”

Section: Statement Of the Problemmentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

See 2 more Smart Citations

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

Belubekyan¹,

Sarkisyan²

2018

Z Angew Math Mech

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show abstract

“…Another option of space problem was investigated in [4]. In work [5] the three-dimensional problems for elastic space waves propagation in isotropic half-space with two options of half-space boundary conditions was researched: free boundary and when we have one shear displacement at the border of halfspace, one of the tangential stress and normal stress is equal to zero. In monograph [6] the summary of elastic waves propagation space problems is given.…”

mentioning

confidence: 99%

Three-dimensional problem of waves propagation in half-space with an elastically restrained boundary.

Sarkisyan¹

2017

Mechanics - Proceedings of National Academy of Sciences of Armenia

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Ключевые слова: упругое полупространство, поверхностная волна, упруго-стеснённая граница Բանալի բառեր. առաձգական կիսատարածություն, մակերևութային ալիքներ, առաձգականորեն կաշկանդված եզր Саркисян С.В. Трёхмерная задача о распространении волн в полупространстве с упруго-стеснённой границей В работе получены дисперсионные уравнения трёхмерной задачи о распространении волн в полупространстве с упруго-стеснённой границей. Исследование задачи упрощается введением потенциальных функций. Показано, что при плоской деформации упругое стеснение границы полупространства приводит к уменьшению степени локализации поверхностной волны. Трёхмерная

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Three-Dimensional Problems of Harmonic Wave Propagation in an Elastic Layer

Cited by 2 publications

References 4 publications

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

Three‐dimensional problem of Rayleigh waves propagating in a half‐space with restrained boundary

Three-dimensional problem of waves propagation in half-space with an elastically restrained boundary.

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