scholarly journals Reflection of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium

10.5772/7424 ◽  
2009 ◽  
Author(s):  
Mahmoud Mohamed
Keyword(s):  
Free Surface ◽  
Plane Waves ◽  
Dissipative Medium

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 Developments in the Reflection of plane waves

2021 ◽  
Vol 23 (07) ◽  
pp. 950-956
Author(s):  
Surbhi Sharma ◽  
◽  
Heena Sharma ◽  
Keyword(s):  
Free Surface ◽  
Initial Stress ◽  
Plane Waves ◽  
Elastic Media ◽  
Basic Equations ◽  
Hydrostatic Initial Stress

The present paper deals with the reflection of plane waves from the free surface. In this paper, we discuss the relatable background of the reflection of plane waves. The basic equations for isotropic and homogeneous generalized thermo-elastic media under hydrostatic initial stress are discussed in the context of thermo-elasticity.

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.

scholarly journals DISCRETE TIME SOLUTION OF PLANE P‐SV WAVES IN A PLANE LAYERED MEDIUM

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 197-219 ◽  
Author(s):  
Clint W. Frasier
Keyword(s):  
Free Surface ◽  
Discrete Time ◽  
Acoustic Waves ◽  
Plane Waves ◽  
Normal Incidence ◽  
Small Time ◽  
Body Waves ◽  
Response Matrix ◽  
Constant Matrix ◽  
P And Sv Waves

For plane waves at normal incidence to a layered elastic medium, both the forward and inverse discrete time problems have been previously solved. In this paper the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at nonnormal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional velocities of each layer. Vertical traveltimes for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment Δτ. This gives a 4×4 layer matrix analogous to the 2×2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses recorded at the free surface of a layered half space are derived as matrix series in integer powers of the Fourier transform variable [Formula: see text]. These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. It is shown that the reflection response matrix generated by a source at the free surface equals the product of a constant matrix and the positive time part of the autocorrelation matrix of the transmission response matrix due to a deep source. This is an extension to nonnormal incidence of a theorem proved by Claerbout for acoustic waves at normal incidence.

Scattering of a Plane Acoustic Wave by a Spherical Elastic Shell Near a Free Surface

1995 ◽  
Author(s):  
H. Huang ◽  
G. C. Gaunaurd
Keyword(s):  
Free Surface ◽  
Separation Of Variables ◽  
Mathematical Problem ◽  
Elastic Shell ◽  
Plane Waves ◽  
Spherical Wave ◽  
Acoustic Scattering ◽  
Scattered Wave ◽  
Image Method ◽  
Spherical Elastic Shell

Abstract The acoustic scattering by a submerged spherical elastic shell near a free surface, and insonified by plane waves at arbitrary angles of incidence is analyzed in an exact fashion using the classical separation of variables technique. To satisfy the boundary conditions at the free surface as well as on the surface of the spherical elastic shell, the mathematical problem is formulated using the image method. The scattering wave fields are expanded in terms of the classical modal series of spherical wave functions utilizing the translational addition theorem. Quite similar to the problem of scattering by multiple spheres, the numerical computation of the scattered wave pressure involves the solution of an ill-conditioned complex matrix system the size of which depends on how many terms of the modal series are required for convergence. This in turn depends on the value of the frequency, and the proximity of the spherical elastic shell to the free surface. The ill-conditioned matrix equation is solved using the Gauss-Seidel iteration method and Twersky’s method of successive iteration double checking each other. Backscattered echoes from the spherical elastic shell are extensively calculated and displayed. The result also demonstrates that the large amplitude low frequency resonances of the echoes of the submerged elastic shell shift upward with proximity to the free surface. This can be attributed to the decrease of added mass for the shell vibration.

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