Rayleigh waves in transversely isotropic thermoelastic diffusive half-space

2008 ◽  
Vol 86 (9) ◽  
pp. 1133-1143 ◽  
Author(s):  
R Kumar ◽  
T Kansal
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Chemical Potential ◽  
Transversely Isotropic ◽  
Surface Wave Propagation ◽  
Surface Displacements ◽  
Special Cases ◽  
Secular Equations ◽  
The Media ◽  
Straight Lines

The present investigation is devoted to the study of the propagation of Rayleigh waves in a homogeneous, transversely isotropic, thermoelastic diffusive half-space subjected to stress-free, thermally insulated and (or) isothermal, and chemical potential boundary conditions, in the context of the theory of coupled thermoelastic diffusion. Secular equations for surface-wave propagation in the media being considered are derived. The surface-particle paths during the motion are found to be elliptical, but degenerate into straight lines in case where there is no phase difference between the horizontal and vertical components of the surface displacements. The phase velocity; attenuation coefficient; specific loss of energy; and the amplitudes of surface displacements, temperature change, and concentration are computed numerically and presented graphically to depict the anisotropy and diffusion effects. Some special cases of frequency equations are also deduced from the present investigation. PACS Nos.: 62.20.–x, 62.20.D–, 62.20.de, 62.20.dj, 62.20.dq, 62.30.+d, 66.10.C–, 66.10.cd, 66.10.cg, 66.30.–h

scholarly journals Wave Propagation in a Micropolar Transversely Isotropic Generalized Thermoelastic Half-Space

2014 ◽  
Vol 19 (2) ◽  
pp. 247-257
Author(s):  
R.R. Gupta
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Rayleigh Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Thermoelastic Properties ◽  
Special Cases ◽  
Generalized Thermoelastic ◽  
Phase Velocity And Attenuation

Abstract Rayleigh waves in a half-space exhibiting microplar transversely isotropic generalized thermoelastic properties based on the Lord-Shulman (L-S), Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories are discussed. The phase velocity and attenuation coefficient in the previous three different theories have been obtained. A comparison is carried out of the phase velocity, attenuation coefficient and specific loss as calculated from the different theories of generalized thermoelasticity along with the comparison of anisotropy. The amplitudes of displacements, microrotation, stresses and temperature distribution were also obtained. The results obtained and the conclusions drawn are discussed numerically and illustrated graphically. Relevant results of previous investigations are deduced as special cases.

Axisymmetric Boussinesq problem of a transversely isotropic half space with surface effects

2018 ◽  
Vol 24 (5) ◽  
pp. 1425-1437 ◽  
Author(s):  
Jing Jin Shen
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Stiffness ◽  
Surface Elasticity ◽  
Transversely Isotropic ◽  
Surface Effects ◽  
Building Blocks ◽  
Material Anisotropy ◽  
Residual Surface Stress ◽  
Special Cases

A transversely isotropic half space with surface effects subjected to axisymmetric loadings is investigated in terms of the Lekhnitskii formulism. Surface effects including residual surface stress and surface elasticity are introduced by using the Gurtin–Murdoch continuum model. With the aid of the Hankel transforms, solutions corresponding to several different axisymmetic loadings are derived and used to determine the influence of surface effects on contact stiffness in nanoindentations. Numerical results are provided to show the influence of surface effects and material anisotropy on the material behaviours. Meanwhile, the obtained analytical Green’s functions for two special cases can be used as building blocks for further mixed boundary value problems.

Propagation of Cylindrical Rayleigh Waves in a Transversly Isotropic Thermoelastic Diffusive Solid Half-Space

2013 ◽  
Vol 43 (3) ◽  
pp. 3-20 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Boundary Conditions ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Attenuation Coefficients ◽  
Special Cases ◽  
Phase Velocity And Attenuation

Abstract The propagation of cylindrical Rayleigh waves in a trans- versely isotropic thermoelastic diffusive solid half-space subjected to stress free, isothermal/insulated and impermeable or isoconcentrated boundary conditions is investigated in the framework of different theories of ther- moelastic diffusion. The dispersion equation of cylindrical Rayleigh waves has been derived. The phase velocity and attenuation coefficients have been computed from the dispersion equation by using Muller’s method. Some special cases of dispersion equation are also deduced

Dispersion Study of Propagation of Torsional Surface Wave in a Layered Structure

2017 ◽  
Vol 33 (3) ◽  
pp. 303-315 ◽  
Author(s):  
S. Gupta ◽  
N. Bhengra
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Boundary Conditions ◽  
Half Space ◽  
Layered Structure ◽  
Transversely Isotropic ◽  
Whittaker Function ◽  
Anisotropic Layer ◽  
Surface Wave Propagation ◽  
Torsional Surface Wave

AbstractThis paper presents the feasibility of torsional surface wave propagation in an anisotropic layer sandwiched between two anisotropic inhomogeneous media. The anisotropy considered in the upper layer and the lower half-space is of transversely isotropic kind while the sandwiched anisotropic layer is a porous layer. The directional rigidities and density have been considered linearly and exponentially varying in the half-space and in the upper layer respectively, while it is taken as a variable in the sandwiched layer. The compact form of dispersion equation governing the propagation of the torsional surface wave has been derived by using the Whittaker function under appropriate boundary conditions. The dispersion of the torsional wave and the effects of inhomogeneity parameters, initial stress and poroelastic constant have been calculated numerically and demonstrated through graphs.

scholarly journals Study of Axi-Symmetric Vibrations in a Micropolar Transversely Isotropic Layer

2019 ◽  
Vol 24 (2) ◽  
pp. 259-268
Author(s):  
R.R. Gupta ◽  
R.R. Gupta
Keyword(s):  
Wave Propagation ◽  
Isotropic Medium ◽  
Lamb Waves ◽  
Transversely Isotropic ◽  
Isotropic Layer ◽  
Transversely Isotropic Medium ◽  
Symmetric Wave ◽  
Special Cases ◽  
Secular Equations ◽  
Transversely Isotropic Layer

Abstract The present investigation deals with the propagation of circular crested Lamb waves in a homogeneous micropolar transversely isotropic medium. Secular equations for symmetric and skew-symmetric modes of wave propagation in completely separate terms are derived. The amplitudes of displacements and microrotation are computed numerically for magnesium as a material and the dispersion curves, amplitudes of displacements and microrotation for symmetric and skew-symmetric wave modes are presented graphically to evince the effect of anisotropy. Some special cases of interest are also deduced.

scholarly journals Dispersion equation of Rayleigh waves in transversely isotropic nonlocal piezoelastic solids half-space

2019 ◽  
Vol 41 (4) ◽  
pp. 363-371
Author(s):  
Do Xuan Tung
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Frequency Parameter ◽  
Free Condition ◽  
Stress Free Boundary

This study is devoted to investigate the propagation of Rayleigh-type waves in transversely isotropic nonlocal piezoelastic half-space.  When the stress-free boundary is maintained at charge-free condition, the dispersion equation for the propagation of Rayleigh waves at the free surface of transversely isotropic piezoelastic solids has been obtained. Based on the obtained dispersion equation, the effect of the nonlocality on the speed of Rayleigh wave is numerically considered. The dependence of velocities of plane waves in transversely isotropic nonlocal piezoelastic medium on the direction of propagation as well as non-dimensional frequency parameter has been also illustrated.

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