Dispersion properties of helical waves in radially inhomogeneous elastic media

2012 ◽  
Vol 131 (6) ◽  
pp. 4263-4271 ◽  
Author(s):  
D. E. Syresin ◽  
T. V. Zharnikov ◽  
V. V. Tyutekin
Keyword(s):  
Elastic Media ◽  
Dispersion Properties ◽  
Inhomogeneous Elastic Media ◽  
Radially Inhomogeneous

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.

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