Elastic Waves in Inhomogeneous Elastic Media

1972 ◽  
Vol 39 (3) ◽  
pp. 696-702 ◽  
Author(s):  
Adnan H. Nayfeh ◽  
Siavouche Nemat-Nasser
Keyword(s):  
Perturbation Method ◽  
Incident Wave ◽  
Elastic Waves ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Time Harmonic ◽  
Special Cases ◽  
Inhomogeneous Elastic Media ◽  
Inhomogeneous Elastic Medium ◽  
Large Frequency

The WKB solution is derived together with the condition for its validity for elastic waves propagating into an inhomogeneous elastic medium. Large frequency expansion solution is also derived. It is found that the WKB solution agrees with that derived for large frequencies when the frequency approaches infinity. Some exact solutions are deduced from the WKB solution. Finally, we consider motions in medium which consists of a material with harmonic periodicity. The solution is obtained by means of a perturbation method. It is shown that, only when the wavelength of the incident wave is small compared with the periodicity-length of the material, the WKB solution constitutes a good approximation. When the wavelength is comparable with this periodicity-length, then, in certain special cases, the material cannot maintain time-harmonic waves; such harmonic waves are not “stable.” These and other solutions are discussed in detail.

Wave Propagation in Layered Elastic Media

1975 ◽  
Vol 42 (1) ◽  
pp. 153-158 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Random Media ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Long Wavelength ◽  
Dispersion Effects ◽  
Special Cases ◽  
Constitutive Representation ◽  
The Waves ◽  
Boltzmann Law ◽  
Layered Elastic Media

The Boltzmann constitutive representation is shown to provide a consistent means of incorporating dispersion effects into the mathematical modeling of wave behavior in layered elastic media. Attention is restricted to long wavelength conditions, with the waves propagating normal to the planes of layering. Special forms of a general Boltzmann law are derived for the special cases of periodic layering and one dimensionally random layering. Although there is no attenuation of harmonic waves in the periodic media case, an analytical representation is obtained for the attenuation measure in random media.

Attenuation of Harmonic Waves in Layered Media

1973 ◽  
Vol 40 (1) ◽  
pp. 155-160 ◽  
Author(s):  
R. M. Christensen
Keyword(s):  
Perturbation Method ◽  
Explicit Formula ◽  
Layered Media ◽  
Harmonic Waves ◽  
Elastic Media ◽  
Attenuation Effect ◽  
The Media ◽  
The Waves ◽  
Periodic Spacing ◽  
Layered Elastic Media

The effective attenuation of harmonic waves propagating through periodically layered elastic media is studied. The waves are taken to be propagating in the direction normal to that of the layering of the media, which has alternate layers of like material. The main restriction of the derivation is that the wavelength of the waves must be long compared with the periodic spacing of the layering. An explicit formula for the attenuation is derived by a perturbation method of analysis. The analysis reveals the basic cause of the attenuation effect in terms of the scattering properties of the medium. Specific examples are studied.

Elastic waves in layered media: Two-scale homogenization approach

2012 ◽  
Vol 23 (6) ◽  
pp. 691-707 ◽  
Author(s):  
V. V. SHELUKHIN ◽  
A. E. ISAKOV
Keyword(s):  
Viscous Fluid ◽  
Elastic Waves ◽  
Wave Speed ◽  
Layered Medium ◽  
Layered Media ◽  
Harmonic Waves ◽  
Time Harmonic ◽  
Homogenization Approach ◽  
Biot Equations

Using the two-scale convergence approach, we derive equations which govern transversal time-harmonic waves through a layered medium taking the form of a poroelastic composite saturated with a viscous fluid. To improve convergence, we construct a corrector. We study how wave speed and attenuation time depend on porosity and frequency. We prove that the Darcy permeability and the acoustic permeability in the Biot equations do not coincide.

Time-Harmonic Waves Propagating Normal to the Layers of Multilayered Periodic Media

1974 ◽  
Vol 41 (1) ◽  
pp. 92-96 ◽  
Author(s):  
Adnan H. Nayfeh
Keyword(s):  
Elastic Modulus ◽  
Dispersion Relation ◽  
Mass Density ◽  
Harmonic Waves ◽  
Periodic Media ◽  
Incident Wavelength ◽  
Time Harmonic ◽  
Periodic Composite ◽  
Special Cases

The dispersion relation is derived for time-harmonic waves propagating normal to the layers of a multilayered periodic composite. The known relations for the homogeneous and the bilaminated media are deduced as special cases. Mixture mass density and elastic modulus are defined in the limit as the ratio of the incident wavelength to the microdimension of the composite approaches infinity.

Dynamic Equivalence of Composite Material and Eigenstrain Problems

1973 ◽  
Vol 40 (2) ◽  
pp. 498-502 ◽  
Author(s):  
P. Wheeler ◽  
T. Mura
Keyword(s):  
Composite Material ◽  
Variational Formulation ◽  
Necessary Conditions ◽  
Mode Shapes ◽  
Homogeneous Material ◽  
Harmonic Waves ◽  
Dynamic Equivalence ◽  
Displacement Mode ◽  
Time Harmonic ◽  
Special Cases

The variational method is employed for determining the displacement mode shapes and dispersion relations for the problem of plane time-harmonic waves propagating through an infinitely extended, periodically arranged composite material. Numerical results are obtained for the special cases of laminated and fiber-reinforced media. Using variational formulation, the composite problem is compared with the problem of a homogeneous material subjected to eigenstrain and body forces. Necessary conditions are developed for the dynamic equivalency of the two problems. Distributions of eigenstrain are shown which yield the same displacement solutions as the problem of a transverse wave propagating normal to the layers of a laminated media.

Reflection and transmission of elastic waves in a system of corrugated layers

1967 ◽  
Vol 57 (3) ◽  
pp. 393-419
Author(s):  
A. Levy ◽  
H. Deresiewicz
Keyword(s):  
Incident Wave ◽  
Elastic Waves ◽  
Scattered Field ◽  
Single Layer ◽  
Body Waves ◽  
Numerical Computations ◽  
Plane Body ◽  
Reflection And Transmission ◽  
Plane Parallel

abstract The scattered field generated by normally incident body waves in a system of layers having small, but otherwise arbitrary, periodic deviations from plane parallel boundaries is shown to consist of superposed plane body and surfacetype waves. Results of numerical computations for two like half-spaces separated by a sinusoidally corrugated single layer, and by two layers, reveal the variation of the amplitude of the field with ratios of velocities, densities, impedances, and with those of depth of layers and wavelength of the boundary corrugations to the wavelength of the incident wave.

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