 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| O. Yu. Dinariev and V. N. Nikolaevskii, "On acoustic resonances in layered media," Mech. Solids. 36 (3), 74-80 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
3 |
Pages |
74-80 |
| Title |
On acoustic resonances in layered media |
| Author(s) |
O. Yu. Dinariev (Moscow)
V. N. Nikolaevskii (Moscow) |
| Abstract |
It is known that an elastic body of finite size
has countably many modes of free vibrations whose frequencies
have a limit point at infinity. Being placed in
a certain infinite medium, this elastic body may lose its spectrum of free
vibrations, in general. However, in many cases, it is possible
to single out free vibration modes for finite inhomogeneities
in an infinite medium and there is an effect of
decaying modes due to the radiation to infinite space,
while the corresponding eigenfrequencies acquire imaginary parts.
In this situation, free vibrations are called acoustic resonances.
The branch of acoustics dedicated to the investigation of
these phenomena is called acoustic spectroscopy
or resonance acoustic spectroscopy [1].
Basic concepts and mathematical techniques of the theory of acoustic resonances
are mostly borrowed from quantum mechanics [2],
where much effort has been applied to the study of resonances.
The present paper contains a number of theoretical and numerical results
concerning resonances in layered elastic media.
The medium is initially assumed infinite, so that the results of
our investigation can be applied to bodies whose total dimension
is much larger than the characteristic dimension of the inhomogeneity.
This approach makes sense for many seismic problems. |
| References |
| 1. | N. D. Veksler, Acoustic Spectroscopy [in Russian], Valgus, Tallinn, 1989. |
| 2. | A. I. Baz', Ya. B. Zel'dovich, and A. M. Perelomov,
Scattering, Reactions, and Decay
in Nonrelativistic Quantum Mechanics [in Russian],
Nauka, Moscow, 1966. |
| 3. | L. M. Brekhovskikh and O. A. Godin,
Acoustics of Layered Media [in Russian], Nauka, Moscow, 1989. |
| 4. | M. V. Fedoryuk, "Asymptotics of
solutions of linear second order differential equations in complex
region," in V. Vasov, Asymptotic Expansions of Solutions of
Ordinary Differential Equations [Russian translation], Mir, Moscow, 1968. |
| 5. | L. Hörmander, Analysis of Linear Partial Differential Operators.
Volume 1. Theory of Distributions and Fourier Analysis [Russian
translation], Mir, Moscow, 1986. |
| 6. | L. Meyer, "Seismic wave propagation in fractured media," in
Mechanics of Jointed and Faulted Rock, pp. 29-38,
Balkena, Rotterdam, 1998. |
|
| Received |
25 March 1999 |
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