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 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.

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

The oscillations of layered elastic media with a wavy boundary

2010 ◽  
Vol 74 (6) ◽  
pp. 633-636 ◽  
Author(s):  
V.A. Babeshko ◽  
O.M. Babeshko ◽  
O.V. Yevdokimova
Keyword(s):  
Elastic Media ◽  
Wavy Boundary ◽  
Layered Elastic Media
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