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.

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.

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.

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 Two-Dimensional Deformation in a Thermoelastic Solid with Microtemperatures Subjected to an Internal Heat Source

2018 ◽  
Vol 23 (1) ◽  
pp. 5-21 ◽  
Author(s):  
P. Ailawalia ◽  
S. Budhiraja ◽  
J. Singh
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

AbstractThe purpose of this paper is to study the two dimensional deformation in a generalized thermoelastic medium with microtemperatures having an internal heat source subjected to a mechanical force. The force is acting along the interface of generalized thermoelastic half space and generalized thermoelastic half space with microtemperatures having an internal heat source. The normal mode analysis has been applied to obtain the exact expressions for the considered variables. The effect of internal heat source and microtemperatures on the above components has been depicted graphically.

scholarly journals On Rayleigh waves in a thinly layered laminated thermoelastic medium with stress couples under initial stresses

1988 ◽  
Vol 1 (3) ◽  
pp. 161-176
Author(s):  
Pijush Pal Roy ◽  
Lokenath Debnath
Keyword(s):  
Phase Velocity ◽  
Initial Stress ◽  
Rayleigh Waves ◽  
Couple Stress ◽  
Frequency Equation ◽  
Initial Stresses ◽  
Displacement Fields ◽  
Thermoelastic Medium ◽  
Couple Stresses

A study is made of the propagation of Rayleigh waves in a thinly layered laminated thermoelastic medium under deviatoric, hydrostatic, and couple stresses. The frequency equation of the Rayleigh waves is obtained. The phase velocity of the Rayleigh waves depends on the initial stress, deviatoric stress, and the couple stress. The laminated medium is first replaced by an equivalent anisotropic thermoelastic continuum. The corresponding thermoelastic coefficients (after deformation) are derived in terms of initially isotropic thermoelastic coefficients (before deformation) of individual layers. Several particular cases are discussed for the determination of the displacement fields with or without the effect of the couple stress.

Analytical solutions of thermo-piezoelectric interactions in a solid fiber of polygonal cross-sections immersed in fluid

2018 ◽  
Vol 14 (3) ◽  
pp. 431-456
Author(s):  
Rajendran Selvamani
Keyword(s):  
Mathematical Model ◽  
Phase Velocity ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Fourier Expansion ◽  
Transversely Isotropic ◽  
Cross Sectional ◽  
Content Type ◽  
Phase Velocity And Attenuation ◽  
Frequency Phase

Purpose The purpose of this paper is to study the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid using the Fourier expansion collocation method. Design/methodology/approach A mathematical model is developed for the analytical study on a transversely isotropic thermo-piezoelectric polygonal cross-sectional fiber immersed in fluid using a linear form of three-dimensional piezothermoelasticity theories. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the Fourier expansion collocation method (FECM) at the irregular boundary surfaces of the polygonal cross-sectional fiber. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots. Findings From the literature survey, it is evident that the analytical formulation of thermo-piezoelectric interactions in a polygonal cross-sectional fiber contact with fluid is not discussed by any researchers. Also, in this study, a polygonal cross-section is used instead of the traditional circular cross-sections. So, the analytical solutions of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid are studied using the FECM. The dispersion curves for non-dimensional frequency, phase velocity and attenuation coefficient are presented graphically for lead zirconate titanate (PZT-5A) material. The present analytical method obtained by the FECM is compared with the finite element method which shows a good agreement with present study. Originality/value This paper contributes the analytical model to find the solution of transversely isotropic thermo-piezoelectric interactions in a polygonal cross-sectional fiber immersed in fluid. The dispersion curves of the non-dimensional frequency, phase velocity and attenuation coefficient are more prominent in flexural modes. Also, the surrounding fluid on the various considered wave characteristics is more significant and dispersive in the hexagonal cross-sections. The aspect ratio (a/b) of polygonal cross-sections is critical to industry or other fields which require more flexibility in design of materials with arbitrary cross-sections.

scholarly journals Propagation of Rayleigh Wave in a Two-Temperature Generalized Thermoelastic Solid Half-Space

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Generalized Thermoelasticity ◽  
Frequency Equation ◽  
Special Cases ◽  
Temperature Parameter ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Two Temperature

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous two-temperature thermoelastic solid half-space in the context of Lord and Shulman theory of generalized thermoelasticity. The governing equations of a two-temperature generalized thermoelastic medium are solved for surface wave solutions. The appropriate particular solutions are applied to the required boundary conditions to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The speed of Rayleigh wave is computed numerically and shown graphically to show the dependence on the frequency and two-temperature parameter.

scholarly journals Uniqueness, reciprocity theorems and plane wave propagation in different theories of thermoelasticy

2013 ◽  
Vol 18 (4) ◽  
pp. 1067-1086
Author(s):  
R. Kumar ◽  
V. Gupta
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Three Dimensional ◽  
P Wave ◽  
Thermoelastic Medium ◽  
Transverse Waves ◽  
Special Cases ◽  
Different Characteristics ◽  
Phase Velocity And Attenuation ◽  
Plane Wave Propagation

Abstract In this work, a compact form of different theories of thermoelasticity is considered. The governing equations for particle motion in a homogeneous isotropic thermoelastic medium are presented. Uniqueness and reciprocity theorems are proved. The plane wave propagation in a homogeneous isotropic thermoelastic medium is studied. For a three dimensional problem there exist four waves, namely a P-wave, two transverse waves (S1, S2) and a thermal wave (T). From the obtained results the different characteristics of waves such as the phase velocity and attenuation coefficient are computed numerically and presented graphically. Some special cases are also discussed.

scholarly journals Propagation of Rayleigh Wave in a Thermoelastic Solid Half-Space with Microtemperatures

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Baljeet Singh
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Half Space ◽  
Frequency Equation ◽  
Rayleigh Surface Wave ◽  
Governing Equations ◽  
Thermoelastic Medium ◽  
Wave Solutions ◽  
Special Cases ◽  
Thermoelastic Solid

The Rayleigh surface wave is studied at a stress-free thermally insulated surface of an isotropic, linear, and homogeneous thermoelastic solid half-space with microtemperatures. The governing equations of the thermoelastic medium with microtemperatures are solved for surface wave solutions. The particular solutions in the half-space are applied to the required boundary conditions at stress-free thermally insulated surface to obtain the frequency equation of the Rayleigh wave. Some special cases are also derived. The non-dimensional speed of Rayleigh wave is computed numerically and presented graphically to reveal the dependence on the frequency and microtemperature constants.

Axi-symmetric deformation in the micropolar porous generalized thermoelastic medium

2010 ◽  
Vol 58 (1) ◽  
pp. 129-139 ◽  
Author(s):  
R. Kumar ◽  
R. Gupta
Keyword(s):  
Normal Force ◽  
Volume Fraction ◽  
Specific Model ◽  
Numerical Inversion ◽  
Thermal Source ◽  
Field Equations ◽  
Thermoelastic Medium ◽  
Symmetric Deformation ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

Axi-symmetric deformation in the micropolar porous generalized thermoelastic mediumIn the present article we studied the thermodynamical theory of micropolar porous material and derived the equations of the linear theory of microploar porous generalized thermoelastic solid. Then the general solution to the field equations for plane axi-symmetric problem are obtained. The Laplace and Hankel transforms have been employed to study the problem, which are inverted numerically by using numerical inversion technique. An application of normal force and thermal source has been taken to show the utility of the approach. The technique developed in the present paper is simple, straightforward and convenient for numerical computation. Effect of micropolarity and porosity on the components of stress, temperature distribution and volume fraction field together with the effect of generalized theory of thermoelasticity have been depicted graphically for a specific model. Some particular cases are also deduced from the present problem.

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