An approximate secular equation of generalized Rayleigh waves in pre-stressed compressible elastic solids

Vinh, Pham Chi; Linh, Nguyen Thi Khanh

doi:10.1016/j.ijnonlinmec.2012.11.004

Cited by 18 publications

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is clear that the H/V ratio χ depends on 9 dimensionless parameters: e k ,ē k (k = 1, 2, 3), r µ , r v and ε which are subjected the inequalities [21] e k > 0,ē k > 0 (k = 1, 2), e 1 e 2 − e 2 3 > 0,ē 1 /ē 2 −ē 2 3 > 0.…”

Section: An Approximate Formulas For the H/v Ratiomentioning

confidence: 99%

See 1 more Smart Citation

An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer

2018

View full text Add to dashboard Cite

This paper is concerned with the propagation of Rayleigh waves in a compressible pre-stressed elastic half-space coated with a thin compressible pre-stressed elastic layer. The main purpose of the paper is to establish an approximate formula for the 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 one of Rayleigh waves at two sides of the interface between the layer and the half-space are created. From the continuity condition at the interface and these relations the displacement amplitude vector of Rayleigh waves at the interface is determined. Then, a third-order approximate formula for the H/V ratio has been derived by expanding the layer displacement amplitude vector at its traction-free surface into Taylor series at the interface. It is shown numerically that the obtained formula is a good approximate one.

show abstract

Section: An Approximate Formulas For the H/v Ratiomentioning

confidence: 99%

“…Note that the H/V ratio χ depends on the dimensionless Rayleigh wave velocity x that is a solution of the secular equation 35in [21] and it depend also on 9 dimensionless parameters mentioned above. When ε = 0, from (43) we have…”

Section: An Approximate Formulas For the H/v Ratiomentioning

confidence: 99%

An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer

2018

View full text Add to dashboard Cite

show abstract

“…In [Vinh and Linh 2012;Vinh et al 2014b] the layer and the half-space are both assumed to be orthotropic and approximate secular equations of third-order were obtained. In [Vinh and Linh 2013] 260 PHAM CHI VINH AND VU THI NGOC ANH the layer and the half-space are both subjected to homogeneous prestrains and an approximate secular equation of third-order was established which is valid for any prestrain and for a general strain energy function.…”

Section: Introductionmentioning

confidence: 99%

Effective boundary condition method and approximate secular equations of Rayleigh waves in orthotropic half-spaces coated by a thin layer

Pham

2016

J. Mech. Mater. Struct.

View full text Add to dashboard Cite

In this paper, the effective boundary condition method for deriving approximate secular equations of Rayleigh waves propagating in elastic half-spaces coated by a thin layer is introduced. Then, the method is used to obtain approximate secular equations of Rayleigh waves in compressible (incompressible) orthotropic half-spaces covered by a thin incompressible (compressible) orthotropic layer. Approximate secular equations of third order have been derived and it is shown that they have high accuracies. Some numerical examples are carried out to evaluate the effect of incompressibility on the Rayleigh wave propagation. It is shown that the incompressibility affects considerably on the Rayleigh wave velocity.

show abstract

An approximate secular equation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer

Pham

2014

Acta Mech

View full text Add to dashboard Cite

An approximate secular equation of generalized Rayleigh waves in pre-stressed compressible elastic solids

Cited by 18 publications

References 17 publications

An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer

An approximate formula for the H/V ratio of Rayleigh waves in compressible pre-stressed elastic half-spaces coated with a thin layer

Effective boundary condition method and approximate secular equations of Rayleigh waves in orthotropic half-spaces coated by a thin layer

An approximate secular equation of Rayleigh waves in an isotropic elastic half-space coated with a thin isotropic elastic layer

Contact Info

Product

Resources

About