 | | 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 |
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| In English (Mech. Solids): | | 4760 |
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| S. N. Kukudzhanov, "Free vibrations of near-cylindrical shells of revolution subjected to preliminary torques and normal pressure," Mech. Solids. 36 (5), 141-145 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
141-145 |
| Title |
Free vibrations of near-cylindrical shells of revolution subjected to preliminary torques and normal pressure |
| Author(s) |
S. N. Kukudzhanov (Tbilisi) |
| Abstract |
Free vibrations of shells of revolution the shape of which is close to
a cylindrical surface are analyzed. The end surfaces of the shells are loaded by
preliminary torques M. The normal pressure q (external or
internal) is uniformly distributed over the shell. We consider the
shells of medium length the generatrix
of the middle surface of which is described by a
parabolic function. On the basis of the theory of shallow
shells, the governing equation of vibrations is obtained. This
equation differs from the familiar one [1] in an additional term
which can coincide in order of magnitude with the other terms. The shells of
both positive and negative Gaussian curvature are considered. Only
principal boundary conditions are taken into account, as is the case for
cylindrical shells. Major attention is paid to the lowest
frequencies which are of the most practical importance. The
solution presented is used to determine the frequency and critical
characteristics. This solution is a good approximation to the
solution for a simply supported shell.
The relations and unified curves are presented, which describe
the dependence of the
lowest frequency and wave mode on the preliminary stresses and
amplitude of the deflection of the shell from a cylindrical surface. It
is shown that if the shell is subjected to preliminary normal and tangential
stresses, then the deflection of the shell from a cylindrical surface (
coinciding with the thickness of the shell
in order of magnitude) can substantially
change the lowest frequencies and wave mode of the shell. |
| References |
| 1. | V. M. Darevskii, "Stability of a near-cylindrical
shell," in Problems of Three-dimensional Structural Design [in
Russian], pp. 35-45, MISI, Moscow, 1980. |
| 2. | V. Z. Vlasov, General Theory of Shells and its Engineering
Applications [in Russian], Gostekhizdat, Moscow, 1976. |
| 3. | A. S. Vol'mir, Stability of Deformable Systems [in
Russian], Fizmatgiz, Moscow, 1967. |
| 4. | S. N. Kukudzhanov, "On the influence of the normal
pressure on the natural frequencies of near-cylindrical shells of
revolution," Izv. AN. MTT [Mechanics of Solids],
No. 6, pp. 121-126, 1996. |
| 5. | S. N. Kukudzhanov, "On the stability of near-cylindrical
shells of revolution simultaneously subjected to torsion and
pressure," Prikl. Mekhanika, Vol. 28, No. 7, pp. 56-62, 1992. |
| 6. | P. E. Tovstic, Stability of Thin Shells [in Russian], Nauka,
Moscow, 1995. |
| 7. | A. I. Molchanov, "Free vibrations of noncircular shells
close to shells of zero Gaussian curvature," Vestnik LGU, Ser. 1,
No. 4, pp. 43-45, 1986. |
|
| Received |
12 January 2000 |
| << Previous article | Volume 36, Issue 5 / 2001 | Next article >> |
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