Rayleigh waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact

Vinh, Pham Chi; Anh, Vu Thi Ngoc

doi:10.1016/j.ijengsci.2013.11.004

Cited by 32 publications

(15 citation statements)

References 30 publications

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“…where c 2 = c 66 /ρ,c 2 = c 66 /ρ. It is clear that the H/V ratio χ depends on 5 dimensionless parameters: e δ ,ē δ , r µ , r v and ε which are subjected the inequalities [19] r…”

Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning

confidence: 99%

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Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017

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This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.Keywords: Rayleigh waves, the Rayleigh wave H/V ratio, incompressible orthotropic elastic half-space, thin incompressible orthotropic elastic layer, approximate formula for the Rayleigh wave H/V ratio.

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“…where c 2 = c 66 /ρ,c 2 = c 66 /ρ. It is clear that the H/V ratio χ depends on 5 dimensionless parameters: e δ ,ē δ , r µ , r v and ε which are subjected the inequalities [19] r…”

Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning

confidence: 99%

“…Note that the Rayleigh wave H/V ratio χ depends on the dimensionless Rayleigh wave velocity x that is a solution of the secular equation (3.14) in [19] and it depends also on 5 dimensionless parameters mentioned above. [20], the exact expressions of displacements in Ref.…”

Section: An Approximate Formulas For the Rayleigh Wave H/v Ratiomentioning

confidence: 99%

Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

2017

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“…Now we can ignore the layer and consider the propagation of Rayleigh waves in the isotropic elastic half-space x 3 ≥ 0 whose surface x 3 = 0 is subjected to the boundary conditions (16), (17). According to Achenbach [21], the displacement components of a Rayleigh wave travelling with velocity c and wave number k in the x 1 -direction and decaying in the x 3 -direction are determined by (6) 1,2 in which U 1 (x 3 ) and U 3 (x 3 ) are given by…”

Section: An Approximate Secular Equation Of Second Ordermentioning

confidence: 99%

“…For obtaining the effective boundary conditions, Achenbach and Keshava [5], Tiersten [6] replaced the thin layer with a plate modeled by different theories: Mindlin's plate theory and the plate theory of low-frequency extension and flexure, while Bovik [7] expanded the stresses at the top surface of the layer into Taylor series in its thickness. The Taylor expansion technique was then developed by Rokhlin and Huang [8,9], Niklasson [10], Benveniste [11], Steigmann and Ogden [12], Ting [13], Vinh and Linh [14,15], Vinh and Anh [16,17], Vinh et al [18].…”

Section: Introductionmentioning

confidence: 99%

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An approximate secular equation of Rayleigh waves in an elastic half-space coated by a thin weakly inhomogeneous elastic layer

Vinh

Anh

2015

Vietnam J. Mech.

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In this paper, the propagation of Rayleigh waves in a homogeneous isotropic elastic half-space coated with a thin weakly inhomogeneous isotropic elastic layer is investigated. The material parameters of the layer is assumed to depend arbitrarily continuously on the thickness variable. The contact between the layer and the half space is perfectly bonded. The main purpose of the paper is to establish an approximate secular equation of the wave. By applying the effective boundary condition method an approximate secular equation of second order in terms of the dimensionless thickness of the layer is derived. It is shown that the obtained approximate secular equation has good accuracy.

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Dynamic Sliding Contact for a Thin Elastic Layer

Kaplunov

Приказчиков

Savšek

2021

Recent Approaches in the Theory of Plates and Plate-Like Structures

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Rayleigh waves in an orthotropic half-space coated by a thin orthotropic layer with sliding contact

Cited by 32 publications

References 30 publications

Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

An approximate secular equation of Rayleigh waves in an elastic half-space coated by a thin weakly inhomogeneous elastic layer

Dynamic Sliding Contact for a Thin Elastic Layer

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