scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

scholarly journals Rotation, Initial Stress, Gravity and Electromagnetic Field Effect on P Wave Reflection from Stress-Free Surface Elastic Half-Space with Voids under Three Thermoelastic Models

2020 ◽  
Vol 22 (1) ◽  
pp. 313-328 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
S. Z. Rida ◽  
R. A. Mohamed ◽  
A. A. Kilany
Keyword(s):  
Free Surface ◽  
Gravity Field ◽  
Initial Stress ◽  
Complex Modulus ◽  
Plane Waves ◽  
Relaxation Times ◽  
Thermal Relaxation ◽  
Generalized Thermoelasticity ◽  
P Wave ◽  
Reflection Coefficients

AbstractThe present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Nihar Sarkar ◽  
Soumen De ◽  
Narayan Das ◽  
Nantu Sarkar
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Half Space ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Energy Ratios ◽  
Thermally Conducting ◽  
Stress Free Boundary

Abstract This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

scholarly journals A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2011
Author(s):  
Mahmoud M. Selim ◽  
Taher A. Nofal
Keyword(s):  
Free Surface ◽  
Reflection Coefficient ◽  
Longitudinal Wave ◽  
Initial Stress ◽  
Half Space ◽  
Seismic Waves ◽  
Initial Stresses ◽  
Reflection Coefficients ◽  
Longitudinal Waves ◽  
Stress Parameter

The aim of this work is to study the behavior of reflection of a longitudinal wave at a free surface of dissipative half-space under the effects of compressive initial stresses. When a longitudinal wave is incident on the free surface of an elastic dissipative half-space, two damped waves (Primarywaves and secondary waves are reflected. Among of these waves, P-waves are affected by compressional initial stresses. The governing equation and corresponding closed-form solutions are derived based on Biot’s incremental deformation theory. The equations of motion are solved analytically and the influence of initial stress parameter on the reflection coefficient of P-wave incidents at the free surface of dissipative half-space is studied in detail. Numerical computations are performed for actual Earth crust and the results analyzing the incident of longitudinal waves are discussed and presented graphically. The analytical solutions and numerical results reveal that the compressive initial stress parameter has notable effects on the reflection coefficient of longitudinal wave incidents on the free surface of dissipative medium. In addition, it has been observed that the presence of compressive initial stresses increases the phase velocity of the longitudinal waves. To the authors’ best knowledge, effects of compressive initial stresses on the reflection coefficients of the incident longitudinal wave on a free surface of dissipative half-space have not been studied before. Since the actual Earth is subject to initial stresses due to different resources, understanding the influences of compressive initial stresses on the reflection coefficient of a longitudinal wave helps seismologists and earthquake engineers to get accurate results of the reflection coefficients of seismic waves propagation in the Earth. Thus, the present study would be useful for seismology and earthquake engineering fields and further study about the nature of seismic waves.

Plane waves in nano-composite materials

2019 ◽  
pp. 198-201
Author(s):  
K. V. Savelieva ◽  
O. G. Dashko ◽  
Y. V. Simchuk
Keyword(s):  
Longitudinal Wave ◽  
Plane Waves ◽  
Wave Interaction ◽  
Elastic Interaction ◽  
Nanocomposite Materials ◽  
Successive Approximations ◽  
Harmonic Waves ◽  
Transverse Waves ◽  
Nonlinear Properties ◽  
Hyper Elastic

The propagation of plane waves in a hyper-elastic medium is theoretically investigated. Two methods of research were used: the method of slowly variable amplitudes and the method of perturbations (successive approximations). The results obtained by these methods are analyzed. The wave interaction in nanocomposite materials is studied. A theoretical study of the cubically nonlinear elastic interaction of plane harmonic waves is carried out for a material whose nonlinear properties are described by the Murnaghan elastic potential. The solution for self-generation of the longitudinal wave is obtained by the method of slowly varying amplitudes. The interaction of transverse horizontally and vertically polarized harmonic waves are studied using the perturbing method. The pumping of energy between different harmonics of a longitudinal wave and various types of transverse waves is described analytically. The results of numerical analysis for various types of nanocomposite materials are presented.

Reflection of Plane Waves in a Rotating Temperature-Dependent Thermoelastic Solid with Diffusion

2012 ◽  
Vol 28 (4) ◽  
pp. 599-606
Author(s):  
B. Singh ◽  
L. Singh ◽  
S. Deswal
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Reflected Waves ◽  
Energy Ratios ◽  
Rotation Parameters ◽  
Thermoelastic Solid

ABSTRACTThe governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing equations indicates the existence of four coupled plane waves in x-z plane. The reflection of plane waves from the free surface of a rotating temperature-dependent thermoelastic solid half-space with diffusion is considered. The required boundary conditions are satisfied by the appropriate potentials for incident and reflected waves in the half-space to obtain a system of four non-homogeneous equations in the reflection coefficients. The expressions for energy ratios of the reflected waves are also obtained. The reflection coefficients and energy ratios are found to depend upon the angle of incidence, reference temperature, thermodiffusion and rotation parameters. Aluminum material is modeled as the half-space to compute the absolute values of the reflection coefficients and the energy ratios. Effects of temperature dependence and rotation parameters on the reflection coefficients and energy ratios are shown graphically for a certain range of the angle of incidence of the incident plane wave.

THE MECHANISM OF GENERATION OF LONG WAVES FROM EXPLOSIONS

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 87-103 ◽  
Author(s):  
C. Hewitt Dix
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Elastic Solid ◽  
Vertical Axis ◽  
Vertical Displacement ◽  
Transverse Waves ◽  
Displacement Potential ◽  
Long Period ◽  
Duhamel Integral ◽  
Ground Roll

Cagniard’s method is applied to the numerical calculation of the vertical displacement due to a point source in a semi‐infinite elastic solid medium at three points on a vertical line through the source. The source is a step in the scalar displacement potential. From these calculated responses the response for any physically possible spherically symmetric source can be computed by application of the Duhamel integral. Clear evidence of backward transmission of transverse wave energy is found along the vertical axis through the source. This, together with the energy of the longitudinal waves, also transmitted backwards, accounts for the mechanism by which energy is held near the source and near the free surface long enough to account for the generation of long period surface waves. This mechanism of generation of long period surface waves is not restricted to the free surface case. Any good reflector, which also generates secondary transverse waves from longitudinal primary waves, will serve the purpose. It is suggested that this gives a clue to the mechanism of the formation of “ground roll” in many practical cases.

Three-wave interaction between transverse and longitudinal waves

1989 ◽  
Vol 42 (1) ◽  
pp. 187-191 ◽  
Author(s):  
G. Brodin ◽  
L. Stenflo
Keyword(s):  
Longitudinal Wave ◽  
Wave Interaction ◽  
Resonant Interaction ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Long Wavelength ◽  
Coupling Phenomena

We consider the resonant interaction between two transverse waves and one longitudinal wave in a plasma. In particular, we discuss coupling phenomena involving long-wavelength modes that have been overlooked by previous authors.

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space

2012 ◽  
Vol 42 (3) ◽  
pp. 33-60 ◽  
Author(s):  
Baljeet Singh ◽  
Anand Yadav
Keyword(s):  
Magnetic Fields ◽  
Half Space ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Thermoelastic Medium ◽  
Reflected Waves ◽  
Velocity Equation ◽  
Thermoelastic Solid

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-SpaceThe governing equations of a rotating transversely isotropic magneto-thermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation, thermal and magnetic fields are shown graphically on these coefficients.

REFLECTION AND TRANSMISSION COEFFICIENTS FOR PLANE WAVES IN ELASTIC MEDIA

Geophysics ◽  
1940 ◽  
Vol 5 (2) ◽  
pp. 115-148 ◽  
Author(s):  
M. Muskat ◽  
M. W. Meres
Keyword(s):  
Incident Energy ◽  
Plane Waves ◽  
Total Reflection ◽  
Interfacial Velocity ◽  
Reflection And Transmission ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Transmission Coefficients ◽  
Elastic Interfaces ◽  
Density Ratios

The results are given of a systematic series of calculations on the coefficients of reflection and transmission for plane waves incident on elastic interfaces. Tables are given for the amplitudes of the reflected and transmitted longitudinal and transverse waves, for the intensities of these components, and for the fractions of the incident energy carried away by them. For incident longitudinal waves calculations were carried out for angles of incidence between 0 and 30 with 5° intervals. For incident transverse waves polarized in the plane of incidence results are given for four angles of incidence up to approximately 16°. For incident transverse waves polarized normal to the plane of incidence the calculations were carried through for all angles of incidence—in steps of 5°—up to total reflection. All the calculations were carried through for interfacial density ratios of 0.7 to 1.3 in steps of 0.1, and interfacial velocity ratios between 0.5 and 2.0 in steps of 0.25.

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