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

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.

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

2011 ◽  
Vol 3 (2) ◽  
pp. 219-238
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Phase Velocity ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Motion ◽  
Thermoelastic Diffusion ◽  
Phase Velocity And Attenuation ◽  
And Diffusion ◽  
Complex Dispersion ◽  
Leaky Rayleigh Waves

AbstractThis paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

Rayleigh waves in generalized thermoelastic medium with mass diffusion

2015 ◽  
Vol 93 (10) ◽  
pp. 1039-1049 ◽  
Author(s):  
Rajneesh Kumar ◽  
Vandana Gupta
Keyword(s):  
Mathematical Model ◽  
Phase Velocity ◽  
Rayleigh Waves ◽  
Polynomial Equation ◽  
Mass Diffusion ◽  
Thermoelastic Medium ◽  
Special Cases ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Phase Velocity And Attenuation

This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic generalized thermoelastic solid half space with mass diffusion in the context of the Lord–Shulman (Lord and Shulman. J. Mech. Phys. Solids. 15, 299 (1967)) and Green–Lindsay (Green and Lindsay. J. Elasticity. 2, 1 (1972)) theories of thermoelasticity. The medium is subjected to stress-free, isothermal, isoconcentrated boundary. After developing a mathematical model, the dispersion curve in the form of a polynomial equation is obtained. The roots of this polynomial equation are verified for not satisfying the original dispersion equation and therefore are filtered out and the remaining roots are checked with the property of decay with depth. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. The behavior of the particle motion is studied for the propagation of Rayleigh waves under Lord–Shulman model. Some special cases are also deduced from the present investigation.

Stoneley and Rayleigh waves in thermoelastic materials with voids

2019 ◽  
Vol 25 (14) ◽  
pp. 2053-2062 ◽  
Author(s):  
SS Singh ◽  
Lalawmpuia Tochhawng
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Surface Waves ◽  
Rayleigh Waves ◽  
Frequency Equation ◽  
Attenuation Coefficients ◽  
Stoneley Waves ◽  
Materials With Voids ◽  
Modes Of Vibration ◽  
Phase Velocity And Attenuation

The present paper deals with the propagation of surface waves (Stoneley and Rayleigh waves) in thermoelastic materials with voids. The frequency equations of the Stoneley waves at the bonded and unbonded interfaces between two dissimilar half-spaces of thermoelastic materials with voids are obtained. The numerical values of the determinant for bonded and unbonded interface are calculated for a particular model. We also derived the frequency equation of the Rayleigh wave in thermoelastic materials with voids. The phase velocity and attenuation coefficients have shown that there are two modes of vibration. These two modes are computed and they are depicted graphically. The effect of thermal parameters in these surface waves is discussed.

scholarly journals Mathematical study of Rayleigh waves in piezoelectric microstretch thermoelastic medium

2019 ◽  
Vol 23 (1) ◽  
pp. 86-93
Author(s):  
Arvind Kumar ◽  
S. M. Abo-Dahab ◽  
Praveen Ailawalia
Keyword(s):  
Mathematical Model ◽  
Phase Velocity ◽  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Polynomial Equation ◽  
Mathematical Study ◽  
Thermoelastic Medium ◽  
Special Cases ◽  
Thermoelastic Solid ◽  
Phase Velocity And Attenuation

Abstract This paper is concerned with the study of propagation of Rayleigh waves in a homogeneous isotropic piezo-electric microstretch-thermoelastic solid half-space. The medium is subjected to stress-free, isothermal boundary. After developing a mathematical model, the dispersion curve in the form of polynomial equation is obtained. Phase velocity and attenuation coefficient of the Rayleigh wave are computed numerically. The numerically simulated results are depicted graphically. Some special cases have also been derived from the present investigation.

Period equation for Rayleigh waves in a layer overlying a half space with a sinusoidal interface

1962 ◽  
Vol 52 (4) ◽  
pp. 807-822 ◽  
Author(s):  
John T. Kuo ◽  
John E. Nafe
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Half Space ◽  
Rayleigh Waves ◽  
Wave Length ◽  
Linear Equations ◽  
Wave Number ◽  
Interface Plane ◽  
Period Equation ◽  
Phase And Group Velocities

abstract The problem of the Rayleigh wave propagation in a solid layer overlying a solid half space separated by a sinusoidal interface is investigated. The amplitude of the interface is assumed to be small in comparison to the average thickness of the layer or the wave length of the interface. Either by applying Rayleigh's approximate method or by perturbating the boundary conditions at the sinusoidal interface, plane wave solutions for the equations which satisfy the given boundary conditions are found to form a system of linear equations. These equations may be expressed in a determinant form. The period (or characteristic) equations for the first and second approximation of the wave number k are obtained. The phase and group velocities of Rayleigh waves in the present case depend upon both frequency and distance. At a given point on the surface, there is a local phase and local group velocity of Rayleigh waves that is independent of the direction of wave propagation.

Rayleigh wave propagation at the boundary surface of dry sandy ($SiO_2$) thermoelastic solids

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shishir Gupta ◽  
Rishi Dwivedi ◽  
Smita Smita ◽  
Rachaita Dutta
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Rayleigh Wave ◽  
Penetration Depth ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Secular Equation ◽  
Rayleigh Surface Wave ◽  
Content Type

Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

scholarly journals The Complex Rayleigh Waves in a Functionally Graded Piezoelectric Half-Space: An Improvement of the Laguerre Polynomial Approach

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2320 ◽  
Author(s):  
Ke Li ◽  
Shuangxi Jing ◽  
Jiangong Yu ◽  
Xiaoming Zhang ◽  
Bo Zhang
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Three Dimensional ◽  
Wave Mode ◽  
Functionally Graded ◽  
Function Technique ◽  
Complex Wave ◽  
Acoustic Wave Devices ◽  
Functionally Graded Piezoelectric

The research on the propagation of surface waves has received considerable attention in order to improve the efficiency and natural life of the surface acoustic wave devices, but the investigation on complex Rayleigh waves in functionally graded piezoelectric material (FGPM) is quite limited. In this paper, an improved Laguerre orthogonal function technique is presented to solve the problem of the complex Rayleigh waves in an FGPM half-space, which can obtain not only the solution of purely real values but also that of purely imaginary and complex values. The three-dimensional dispersion curves are generated in complex space to explore the influence of the gradient coefficients. The displacement amplitude distributions are plotted to investigate the conversion process from complex wave mode to propagating wave mode. Finally, the curves of phase velocity to the ratio of wave loss decrements are illustrated, which offers extra convenience for finding the high phase velocity points where the complex wave loss is near zero.

Analysis of gravity and non-homogeneity on Rayleigh wave in anisotropic elastic-viscoelastic half space of higher order

2015 ◽  
Vol 11 (1) ◽  
pp. 120-130 ◽  
Author(s):  
Rajneesh Kakar
Keyword(s):  
Phase Velocity ◽  
Half Space ◽  
Rayleigh Waves ◽  
Mass Density ◽  
Wave Number ◽  
Inhomogeneous Layer ◽  
Third Order ◽  
Content Type ◽  
Anisotropic Elastic ◽  
Mathematical Techniques

Purpose – The purpose of this paper is to illustrate the propagation of Rayleigh waves in an anisotropic inhomogeneous layer placed over an isotropic gravitational viscoelastic half space of third order. Design/methodology/approach – It is considered that the mass density and the elastic coefficients of the layer are space dependent. Dispersion properties of waves are derived with the simple mathematical techniques. Graphs are plotted between phase velocity ‘k’ and wave number ‘c’ for different values of inhomogeneity parameters for a particular model and the effects of inhomogeneity and gravity are studied. Findings – The wave analysis indicates that the phase velocity of Rayleigh waves is affected quite remarkably by the presence of inhomogeneity, gravity and strain rates of strain parameters in the half space. The effects of inhomogeneity and depth on the phase velocity are also shown in corresponding figures. Originality/value – The results presented in this study may be attractive and useful for mathematicians, seismologists and geologists.

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

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