 | | 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
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| S. V. Novotny, "Generalization of the Pochhammer-Chree problem to the case of an inertially compliant boundary," Mech. Solids. 37 (3), 89-100 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
89-100 |
| Title |
Generalization of the Pochhammer-Chree problem to the case of an inertially compliant boundary |
| Author(s) |
S. V. Novotny (Moscow) |
| Abstract |
A solution of the internal regular problem of propagation
of stationary axially symmetric plane waves in an infinite isotropic
circular cylinder (the problem of Pochhammer-Chree [1], [2]) is considered
under boundary conditions of inertial type, i. e., the stresses on the
boundary are proportional to the accelerations.
We obtain the corresponding frequency relation which determines the
dispersion law in the presence a stiffened boundary. This relation is
examined for real and imaginary propagation parameters and is compared
with solutions satisfying the classical boundary conditions.
Qualitative distinctions are detected in the structure of the frequency
spectrum as compared with the case of free boundary. We also describe how
and to which extent the principal spectral characteristics of the harmonic
wave process depend on the stiffening parameter and Poisson's ratio. |
| References |
| 1. | L. Pochhammer,
"Über die Fortpflanzungsgeschwindigkeiten kleiner Schwingungen
in einem unbegrenzten isotropen Kreiszylinder," J. Reine und Angew.
Bd. 81, S. 324-336, 1876. |
| 2. | C. Chree,
"The equations of an isotropic elastic solid in polar and cylindrical coordinates,
their solutions and applications," Trans. Cambridge Phil. Soc., Vol. 14,
pp. 250-369, 1889. |
| 3. | A. Love, A Treatise on the Mathematical Theory of Elasticity [Russian translation],
ONTI, Leningrad, 1935. |
| 4. | M. Onoe, H. D. McNiven, and R. D. Mindlin, "Dispersion of
axially symmetric waves in elastic rods," Trans. ASME. Appl. Mech.,
Vol. 62, No. 4, pp. 139-145, 1962. |
| 5. | T. R. Meeker and A. H. Meitzler,
"Wave propagation in rods and plates,"
in W. P. Mason (Editor), Physical Acoustics. Volume 1. Methods and Devices.
Part A, pp. 140-203, New York, London, 1964. |
| 6. | J. Miklowitz, The Theory of Elastic Waves and Waveguides,
North-Holland, Amsterdam, 1978. |
| 7. | V. T. Grinchenko and V. V. Meleshko,
Harmonic Vibrations and Waves in Elastic Bodies [in Russian], Naukova Dumka, Kiev,
1981. |
| 8. | S. V. Novotny, "Stationary torsional waves in a cylinder whose boundary
has limited compliance," Vestnik MGU [Bulletin of Moscow State
University], Ser. 1, Mat., Mekh., No. 4, pp. 77-85, 1996. |
| 9. | J. Zemanek, "An experimental and theoretical investigation of
elastic wave propagation in a cylinder," J. Acoust. Soc.Amer.,
Vol. 51, No. 1, Pt. 2, pp. 265-283, 1972. |
| 10. | D. Bancroft, "The velocity of longitudinal waves
in cylindrical bars," Phys. Rev., Vol. 59, pp. 588-593, 1941. |
| 11. | Y. H. Pao and R. D. Mindlin,
"Dispersion of flexural waves in an elastic circular cylinder,"
Trans. ASME, Ser. E., J. Appl. Mech., Vol. 27, No. 3, pp. 513-520, 1960. |
| 12. | R. Sinclair,
"Velocity dispersion of Rayleigh waves propagating along
rough surfaces. Part 2," J. Acoust. Soc. Amer., Vol. 50, No. 3,
pp. 841-845, 1971. |
|
| Received |
22 September 2000 |
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