scholarly journals Propagation of Waves at an Interface between a Liquid Half-Space and an Orthotropic Micropolar Solid Half-Space

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Baljeet Singh ◽  
Ritu Sindhu
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Present Model ◽  
Angle Of Incidence ◽  
Longitudinal Displacement ◽  
Amplitude Ratios ◽  
Displacement Wave ◽  
Solutions Of Equations ◽  
Propagation Of Waves ◽  
Refracted Waves

An inviscid liquid half-space is considered in welded contact with a orthotropic micropolar solid half-space. Appropriate plane harmonic solutions of equations governing a liquid half-space and an orthotropic solid half-space are obtained. These solutions satisfy the required boundary conditions at the interface to obtain a system of four nonhomogeneous equations in amplitude ratios for incident quasi-longitudinal displacement wave. The amplitude ratios of various reflected and refracted waves are computed numerically for a particular example of the present model. The effect of anisotropy upon these amplitude ratios is shown graphically for a particular range of the angle of incidence.

scholarly journals Reflection of Plane Waves from Surface of a Generalized Thermo-Viscoelastic Porous Solid Half-Space with Impedance Boundary Conditions

2020 ◽  
Vol 22 (4) ◽  
pp. 1483-1496
Author(s):  
Baljeet Singh
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Impedance Boundary ◽  
Reflected Waves ◽  
Material Parameters ◽  
Impedance Boundary Conditions ◽  
Impedance Parameter

AbstractA phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x–z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.

scholarly journals Reflection at Free Surface in Micropolar Thermoelastic Solid with two Temperatures

2013 ◽  
Vol 18 (1) ◽  
pp. 217-234 ◽  
Author(s):  
K. Sharma
Keyword(s):  
Half Space ◽  
Plane Surface ◽  
Plane Waves ◽  
Relaxation Times ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Two Temperatures ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

The present investigation is concerned with the effect of two temperatures on reflection coefficients in a micropolar thermoelastic solid half space. With two relaxation times, reflection of plane waves impinging obliquely at a plane interface of the micropolar generalized thermoelastic solid half space with two temperatures is investigated. The incident wave is assumed to be striking at the plane surface after propagating through the micropolar generalized thermoelastic solid with two temperatures. Amplitude ratios of the various reflected waves are obtained in closed form and it is found that these are functions of angle of incidence, frequency and are affected by the elastic properties of the media. The effect of two temperatures is shown on these amplitude ratios for a specific model.

scholarly journals The Effects of Piezoelectricity on the Interaction of Waves in Fluid-Loaded Poroelastic Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Vishakha Gupta ◽  
Anil K. Vashishth
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Constitutive Equations ◽  
Vertical Component ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Solid Interface ◽  
Interaction Of Waves ◽  
Electric Potentials

The effects of piezoelectricity on the interaction of waves at fluid-poroelastic interface are studied. The constitutive equations and governing equations are formulated and their solution is obtained. The boundary conditions are described at fluid-solid interface. The effects of various parameters on the angle of refraction, amplitude ratios, displacements, electric potentials, and vertical component of slowness are studied numerically for a particular model. The results obtained are in agreement with the general laws of physics.

Propagation of Elastic Waves at Micropolar Viscoelastic Solid/Fluid-Saturated Incompressible Porous Solid Interface

2018 ◽  
Vol 15 (08) ◽  
pp. 1850076 ◽  
Author(s):  
M. S. Barak ◽  
Vinod Kaliraman
Keyword(s):  
Half Space ◽  
Incident Wave ◽  
Plane Surface ◽  
Elastic Solid ◽  
Specific Model ◽  
Porous Solid ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Viscoelastic Solid ◽  
Micropolar Viscoelastic Solid

The present paper concerned with the reflection and transmission of plane wave from a plane surface separating a micropolar viscoelastic solid (MVES) half-space and a fluid-saturated (FS) incompressible porous solid half-space is studied. A longitudinal wave ([Formula: see text]-wave) or transverse wave (SV-wave) impinges obliquely at the interface. Amplitude ratios for various reflected and transmitted waves have been obtained with the help of boundary conditions at the interface. Then, these amplitude ratios have been computed numerically for a specific model and results thus obtained are shown graphically with the angle of incidence of the incident wave. It is found that these amplitude ratios depend on the angle of incidence of the incident wave as well as on the properties of media. From the present investigation, a special case, when FS porous half-space reduces to empty porous solid and MVES half-space reduces to micropolar elastic solid, has also been deduced and discussed with the help of graphs.

Reflection and Refraction of Longitudinal Displacement Wave at Interface between Two Micropolar Elastic Solid

2010 ◽  
Vol 139-141 ◽  
pp. 214-217 ◽  
Author(s):  
Bing Bing Xue ◽  
Hong Yu Xu ◽  
Zhu Mu Fu ◽  
Qing Yong Sun
Keyword(s):  
Elastic Solid ◽  
Theory Model ◽  
Type Ii ◽  
Longitudinal Displacement ◽  
Amplitude Ratios ◽  
Reflection And Refraction ◽  
Displacement Wave ◽  
Viscoelastic Theory ◽  
Voigt Model ◽  
Coupled Theory

Using the model of generalized micropolar magneto-thermo-elasticity, reflection and refraction of longitudinal displacement wave at interface of two welded micropolar elastic media are studied. The model can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. And if some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. Using continuous conditions at the interface, the amplitude ratios of reflected and refracted micropolar magneto-thermoelastic longitudinal displacement waves, longitudinal microrotational waves and the coupled transverse and microrotational waves are studied for incident longitudinal displacement wave. The numerical results show that the effect of magnetic field is very significant on the amplitude ratios.

Propagation Characteristics of Longitudinal Displacement Wave in Micropolar Fluid with Micropolar Elastic Plate

2011 ◽  
Vol 694 ◽  
pp. 923-927 ◽  
Author(s):  
Qing Yong Sun ◽  
Hong Yu Xu ◽  
Bin Liang
Keyword(s):  
Transmission Coefficient ◽  
Elastic Plate ◽  
Micropolar Fluid ◽  
Incident Angle ◽  
Angle Of Incidence ◽  
Longitudinal Displacement ◽  
Reflection And Transmission ◽  
Variation Characteristics ◽  
Displacement Wave ◽  
Fluid Theory

Based on micropolar fluid theory and micropolar solid elasticity theory, reflection and transmission characteristics of three kinds of micropolar elastic waves, which are longitudinal displacement wave and two coupled waves, were studied when incident longitudinal displacement wave propagated in micropolar fluid with micropolar elastic plate. Using numerical example, the variations of various amplitudes are also shown against the angle of incidence and the variation characteristics of various amplitudes are discussed. Results show that there exist maximum values of reflection and transmission coefficient for coupled wave, however, there exist minimum values of reflection coefficient for longitudinal displacement wave, and transmission coefficient decreases with the incident angle and the transmission coefficient are smaller for bigger incident angle.

scholarly journals Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Narottam Maity ◽  
S. P. Barik ◽  
P. K. Chaudhuri
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Uniform Magnetic Field ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Longitudinal Displacement ◽  
Amplitude Ratios ◽  
Wave Velocities ◽  
Generalized Thermoelastic ◽  
The Magnetic Field

Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically.

scholarly journals Effect of Rotation on Propagation of Waves in Transversely Isotropic Thermoelastic Half-Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Raj Rani Gupta ◽  
Rajani Rani Gupta
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Thermal Wave ◽  
Isotropic Medium ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transversely Isotropic Medium ◽  
Propagation Of Waves

The present study is concerned with the effect of rotation on the propagation of plane waves in a transversely isotropic medium in the context of thermoelasticity theory of GN theory of types II and III. After solving the governing equations, three waves propagating in the medium are obtained. The fastest among them is a quasilongitudinal wave. The slowest of them is a thermal wave. The remaining is called quasitransverse wave. The prefix “quasi” refers to their polarizations being nearly, but not exactly, parallel or perpendicular to the direction of propagation. The polarizations of these three waves are not mutually orthogonal. After imposing the appropriate boundary conditions, the amplitudes of reflection coefficients have been obtained. Numerically simulated results have been plotted graphically with respect to frequency to evince the effect of rotation and anisotropy.

scholarly journals Reflection and transmission of elastic waves at viscous liquid/micropolar elastic solid interface

2001 ◽  
Vol 26 (11) ◽  
pp. 685-694 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sushil K. Tomar
Keyword(s):  
Viscous Liquid ◽  
Half Space ◽  
Incident Wave ◽  
Elastic Waves ◽  
Elastic Solid ◽  
Specific Model ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflection And Transmission ◽  
Special Case

Amplitude ratios of various reflected and transmitted elastic waves from a plane interface separating a viscous liquid half-space and a micropolar elastic solid half-space, are obtained in two cases (i) when longitudinal wave propagating through the solid half-space is made incident at the interface and (ii) when “coupled-wave” propagating through the solid half-space is made incident at the interface. These amplitude ratios have been computed numerically for a specific model and results obtained are presented graphically. It is found that these amplitude ratios depend on the angle of incidence of the incident wave and the effect of viscosity of the liquid on amplitude ratios is noticed. The problem studied by Tomar and Kumar (1995) has been reduced as a special case of our problem.

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