Attenuation of Harmonic Waves in Layered 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.

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Wave Propagation in Layered Elastic Media

Journal of Applied Mechanics ◽

10.1115/1.3423507 ◽

1975 ◽

Vol 42 (1) ◽

pp. 153-158 ◽

Cited By ~ 15

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.

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Elastic Waves in Inhomogeneous Elastic Media

Journal of Applied Mechanics ◽

10.1115/1.3422775 ◽

1972 ◽

Vol 39 (3) ◽

pp. 696-702 ◽

Cited By ~ 12

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.

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Elastic Dispersion, Homogeneous Dispersive Media and an Application to Periodic Elastic Media

Journal of Applied Mechanics ◽

10.1115/1.3424298 ◽

1978 ◽

Vol 45 (2) ◽

pp. 337-342

Author(s):

G. N. Balanis

Keyword(s):

Energy Loss ◽

Wave Dispersion ◽

Inhomogeneous Media ◽

Dispersive Media ◽

Elastic Media ◽

The Media ◽

Propagation Of Waves ◽

The Waves

Wave dispersion that occurs without energy loss is examined and media capable of supporting waves with such dispersion are developed. The media are homogeneous and dispersive. The dispersion of the waves they generate shares many of the characteristics of the dispersion of waves propagating through inhomogeneities. Thus these media can be useful in modeling the propagation of waves in inhomogeneous media. An example supporting the utility of modeling applications is presented.

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