Extensional and Transversal Wave Motion in Transversely Isotropic Thermoelastic Plates by Using Asymptotic Method

2011 ◽  
Vol 78 (6) ◽  
Author(s):  
J. N. Sharma ◽  
P. K. Sharma ◽  
S. K. Rana
Keyword(s):  
Phase Velocity ◽  
Asymptotic Method ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Transverse Motion ◽  
Transversal Wave ◽  
Thermoelastic Plates ◽  
Special Cases ◽  
Thermoelastic Plate

The present investigation is concerned with the study of extensional and transversal wave motions in an infinite homogenous transversely isotropic, thermoelastic plate by using asymptotic method in the context of coupled thermoelasticity, Lord and Shulman (1967, “The Generalized Dynamical Theory of Thermoelasticity,” J. Mech. Phys. Solids, 15, pp. 299–309), and Green and Lindsay (1972, “Thermoelasticity,” J. Elast., 2, pp. 1–7) theories of generalized thermoelasticity. The governing equations for extensional, transversal, and flexural motions have been derived from the system of three-dimensional dynamical equations of linear thermoelasticity. The asymptotic operator plate model for extensional motion in a homogeneous transversely isotropic thermoelastic plate leads to sixth degree polynomial secular equation that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion. The Rayleigh–Lamb frequency equation for the plate is expanded in power series in order to obtain polynomial frequency equation and velocity dispersion relations. Their validation has been established with that of asymptotic method. The special cases of short and long wavelength waves are also discussed. The expressions for group velocity of extensional and transversal modes have been derived. Finally, the numerical solution is carried out for homogeneous transversely isotropic plate of single crystal of zinc material. The dispersion curves of phase velocity and attenuation coefficient are presented graphically.

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.

Influence of Rigid, Stress-Free and Yielding Base of a Composite Structure on the Propagation of Rayleigh-Type Wave: A Comparative Approach

2017 ◽  
Vol 34 (6) ◽  
pp. 733-748
Author(s):  
A. Chattopadhyay ◽  
A. K. Verma ◽  
M. S. Chaki ◽  
A. K. Singh
Keyword(s):  
Composite Structure ◽  
Transversely Isotropic ◽  
Frequency Equation ◽  
Comparative Approach ◽  
Width Ratio ◽  
Type Wave ◽  
Special Cases ◽  
Layer Medium ◽  
Velocity Equation ◽  
The Comparative Study

AbstractIn this paper, case wise studies have been made to investigate the possibility of propagation of Rayleigh-type wave in a composite structure comprised of two transversely-isotropic material layers with viscoelastic effect. The common interface between the layers is considered to be rigid whereas the base has been considered as rigid, stress-free and yielding in three different cases (Case-I, II and III). Closed-form of frequency equation and damped velocity equation has been established analytically for propagation of Rayleigh-type wave in a composite structure for all three cases. In special cases, frequency equations and damped velocity equations for the case of composite structure with rigid, stress-free and yielding base have been found in well-agreement to the established standard results pre-existing in the literature. Numerical and graphical computation of phase and damped velocity of Rayleigh-type wave propagating in the composite structure comprised of double transversely-isotropic viscoelastic Taylor sandstone material layers (Model-I) and double isotropic viscoelastic material layers (Model-II) have been carried out. Significant effect of anisotropy and width ratio of layers, dilatational and volume viscoelasticity associated with viscoelasticity of layer medium and yielding parameter associated with yielding base of composite structure on phase and damped velocities of Rayleigh-type wave for the considered models have been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the present problem.

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 Propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses

1988 ◽  
Vol 1 (4) ◽  
pp. 271-286 ◽  
Author(s):  
Lokenath Debnath ◽  
Pijush Pal Roy
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Couple Stress ◽  
Frequency Equation ◽  
Initial Stresses ◽  
Wave Number ◽  
Edge Waves ◽  
Approximate Representation ◽  
Couple Stresses ◽  
Special Cases

The propagation of edge waves in a thinly layered laminated medium with stress couples under initial stresses is examined. Based upon an approximate representation of a laminated medium by an equivalent anisotropic continuum with average initial and couple stresses, an explicit form of frequency equation is obtained to derive the phase velocity of edge waves. Edge waves exist under certain conditions. The inclusion of couple stresses increases the velocity of wave propagation. For a specific compression, the presence of couple stresses increases the velocity of wave propagation with the increase of wave number, whereas the reverse is the case when there is no couple stress. Numerical computation is performed with graphical representations. Several special cases are also examined.

Forced Flexural Vibrations in a Thin Nonlocal Rectangular Plate with Kirchhoff’s Thin Plate Theory

2020 ◽  
Vol 20 (09) ◽  
pp. 2050107
Author(s):  
Iqbal Kaur ◽  
Parveen Lata ◽  
Kulvinder Singh
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Small Scale ◽  
Concentrated Load ◽  
Thin Rectangular Plate ◽  
Flexural Vibrations

This study deals with a novel model of forced flexural vibrations in a transversely isotropic thermoelastic thin rectangular plate (TRP) due to time harmonic concentrated load. The mathematical model is prepared for the thin plate in a closed form with the application of Kirchhoff’s love plate theory for nonlocal generalized thermoelasticity with Green–Naghdi (GN)-III theory of thermoelasticity. The nonlocal thin plate has a nonlocal parameter to depict small-scale effect. The double finite Fourier transform technique has been used to find the expressions for lateral deflection, thermal moment and temperature distribution for simply supported (SS) thin rectangular plate in the transformed domain. The effect of classical thermoelasticity (CTE) theory of thermoelasticity and nonlocal parameters has been shown on the computed quantities. Few particular cases have also been deduced.

Do traveltimes in pulse‐transmission experiments yield anisotropic group or phase velocities?

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1774-1779 ◽  
Author(s):  
Joe Dellinger ◽  
Lev Vernik
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Elastic Constants ◽  
Near Field ◽  
Frequency Dispersion ◽  
Transversely Isotropic ◽  
Sh Waves ◽  
Phase Velocities ◽  
Pulse Transmission ◽  
Transmission Technique

The elastic properties of layered rocks are often measured using the pulse through‐transmission technique on sets of cylindrical cores cut at angles of 0, 90, and 45 degrees to the layering normal (e.g., Vernik and Nur, 1992; Lo et al., 1986; Jones and Wang, 1981). In this method transducers are attached to the flat ends of the three cores (see Figure 1), the first‐break traveltimes of P, SV, and SH‐waves down the axes are measured, and a set of transversely isotropic elastic constants are fit to the results. The usual assumption is that frequency dispersion, boundary reflections, and near‐field effects can all be safely ignored, and that the traveltimes measure either vertical anisotropic group velocity (if the transducers are very small compared to their separation) or phase velocity (if the transducers are relatively wide compared to their separation) (Auld, 1973).

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.

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