On Higher Order Effective Boundary Conditions for a Coated Elastic Half-Space

2018 ◽  
pp. 449-462 ◽  
Author(s):  
Julius Kaplunov ◽  
Danila Prikazchikov ◽  
Leyla Sultanova
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Elastic Half Space ◽  
Higher Order ◽  
Effective Boundary ◽  
Effective Boundary Conditions

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.

Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies

2007 ◽  
Vol 463 (2085) ◽  
pp. 2223-2239 ◽  
Author(s):  
T.C.T Ting
Keyword(s):  
Boundary Conditions ◽  
Thin Layer ◽  
Elastic Body ◽  
Elastic Layer ◽  
Elastic Half Space ◽  
The Body ◽  
Thin Layers ◽  
Effective Boundary ◽  
Effective Boundary Conditions ◽  
Anisotropic Elastic

When a very thin elastic layer is bonded to an elastic body, it is desirable to have effective boundary conditions for the interface between the layer and the body that take into account the existence of the layer. In the literature, this has been done for special anisotropic elastic layers. We consider here the layer that is a general anisotropic elastic material. The mechanics of a thin layer is studied for elastostatics as well as steady state waves. It is shown that one-component surface waves cannot propagate in a semi-infinite thin layer. We then present Love waves in an anisotropic elastic half-space bonded to a thin anisotropic elastic layer. The dispersion equation so obtained is valid for long wavelength. Finally, effective boundary conditions are presented for two thin layers bonded to two surfaces of a plate and a thin layer bonded between two anisotropic elastic half-spaces.

Influence of wall roughness on the slip behaviour of viscous fluids

2008 ◽  
Vol 138 (5) ◽  
pp. 957-973 ◽  
Author(s):  
Dorin Bucur ◽  
Eduard Feireisl ◽  
Šárka Nečasová
Keyword(s):  
Boundary Condition ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Limit Problem ◽  
Viscous Fluids ◽  
Wall Roughness ◽  
Effective Boundary ◽  
Specific Direction ◽  
Friction Term ◽  
Effective Boundary Conditions

We consider the stationary equations of a general viscous fluid in an infinite (periodic) slab supplemented with Navier's boundary condition with a friction term on the upper part of the boundary. In addition, we assume that the upper part of the boundary is described by a graph of a function φε, where φε oscillates in a specific direction with amplitude proportional to ε. We identify the limit problem when ε → 0, in particular, the effective boundary conditions.

Rayleigh-type surface wave on a rotating orthotropic elastic half-space with impedance boundary conditions

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1980-1987
Author(s):  
Baljeet Singh ◽  
Baljinder Kaur
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Half Space ◽  
Rotation Rate ◽  
Secular Equation ◽  
Elastic Half Space ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions

The propagation of Rayleigh type surface waves in a rotating elastic half-space of orthotropic type is studied under impedance boundary conditions. The secular equation is obtained explicitly using traditional methodology. A program in MATLAB software is developed to obtain the numerical values of the nondimensional speed of Rayleigh wave. The speed of Rayleigh wave is illustrated graphically against rotation rate, nondimensional material constants, and impedance boundary parameters.

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