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

Wave Motion ◽  
2012 ◽  
Vol 49 (7) ◽  
pp. 681-689 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Secular Equation ◽  
Elastic Half Space

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

2015 ◽  
Vol 37 (1) ◽  
pp. 71-80
Author(s):  
Pham Chi Vinh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Effective Boundary ◽  
Inhomogeneous Elastic Layer ◽  
Boundary Condition Method ◽  
Effective Boundary Condition ◽  
Thickness Variable

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.

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

2017 ◽  
Vol 39 (4) ◽  
pp. 365-374
Author(s):  
Pham Chi Vinh ◽  
Tran Thanh Tuan ◽  
Le Thi Hue
Keyword(s):  
Free Surface ◽  
Rayleigh Wave ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Layer ◽  
Approximate Formula ◽  
Elastic Half Space ◽  
Displacement Amplitude ◽  
Vertical Displacements ◽  
Thin Elastic Layer

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.

scholarly journals Rayleigh waves in compressible orthotropic half-space overlaid by a thin un-coaxial orthotropic layer

2021 ◽  
Vol 15 (4) ◽  
pp. 54-64
Author(s):  
Trinh Thi Thanh Hue ◽  
Phan Thi Thu Phuong ◽  
Pham Hong Anh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Traditional Approach ◽  
Elastic Half Space ◽  
Third Order ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
Thin Elastic Layer

The problem of Rayleigh waves in compressible orthotropic elastic half-space overlaid by a thin elastic layer of which principal material axes are coincident have been researched by many scientists. However, the problem with the conditions that the half-space and the layer have only one common principal material axis that perpendicular to the layer while the remains are not identical has not gotten enough attention. This paper presents a traditional approach to obtain an approximate secular equation by approximately replacing the thin layer by effective boundary conditions of third-order. The wave then is considered as a Rayleigh wave propagating in an orthotropic half-space, without coating, subjected to the effective boundary conditions. This explicit approximate secular equation is potentially useful in non-damage assessment studies.

On a technique for deriving explicit transfer matrices of orthotropic layers

2015 ◽  
Vol 37 (4) ◽  
pp. 303-315 ◽  
Author(s):  
Pham Chi Vinh ◽  
Nguyen Thi Khanh Linh ◽  
Vu Thi Ngoc Anh
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Half Space ◽  
Transfer Matrix ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Transfer Matrices ◽  
Orthotropic Layer ◽  
Wave Propagation Problem ◽  
Arbitrary Thickness

This paper presents  a technique by which the transfer matrix in explicit form of an orthotropic layer can be easily obtained. This transfer matrix is applicable for both the wave propagation problem and the reflection/transmission problem. The obtained transfer matrix is then employed to derive the explicit secular equation of Rayleigh waves propagating in an orthotropic half-space coated by an orthotropic layer of arbitrary thickness.

Sign in / Sign up

Export Citation Format

Share Document