 | | 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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| E. Z. Korol', "On eigenfrequencies of small longitudinal and transverse vibrations of thin orthotropic circular plates," Mech. Solids. 36 (2), 138-147 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
2 |
Pages |
138-147 |
| Title |
On eigenfrequencies of small longitudinal and transverse vibrations of thin orthotropic circular plates |
| Author(s) |
E. Z. Korol' (Moscow) |
| Abstract |
Models of cylindrically orthotropic circular plates are widely used
for the strength analysis of reflector antennas, laser devices, etc.
Exact solutions for problems of axially symmetric bending of
isotropic plates are given in [1-3]; solutions in the general case
are obtained in works authored or co-authored by
E. Z. Korol' [E. Z. Korol',
"Boundary value problems of bending of cylindrically orthotropic circular
plates on an elastic inhomogeneous foundation," in
Book of Abstracts.
4th Intern. Conf. on Mechanics of Inhomogeneous Structures,
pp. 165-166, Ternopol, 1995;
E. I. Grigolyuk, E. Z. Korol', and M. E. Izmailova,
"Bending of thin orthotropic circular plates on an elastic foundation,"
NII Mekhaniki MGU, Moscow, 1997 (Dep. VINITI 7 October 1997,
No. 2997, B-97); E. Z. Korol', "Fundamental system of solutions of
nth order differential equations of Bessel type and their applications
in mechanics of solids. Part 1. Cylindrical functions of the nth order.
Generalization of the Neumann-Weber-Schläfli formulas,"
NII Mekhaniki MGU, Moscow, 1998 (Dep. VINITI
3 April 1998, No. 990, B-98).],
whereas no solutions are known for the problems of longitudinal and
transverse vibrations of general type. |
| References |
| 1. | A. N. Dinnik, Applications of Bessel Functions in Elasticity
Problems. Part 1 [in Russian], Izd-vo NPI, Novocherkassk, 1913. |
| 2. | B. G. Korenev, Introduction to the Theory of Bessel Functions [in Russian],
Nauka, Moscow, 1971. |
| 3. | E. B. Kuznetsov and V. I. Shalashilin,
"Free vibrations and stability of circular plates subjected to axially symmetric
heating," Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 147-151,
1975. |
| 4. | E. T. Whittaker and J. N. Watson,
A Course of Modern Analysis. Volume 2 [Russian translation],
Fizmatgiz, Moscow, 1955. |
| 5. | H. Weber, "Über eine Darstellung willkurlicher Funktionen
durch Bessel'sche Funktionen," Math. Ann., Bd. 6, S. 146-161, 1873. |
| 6. | L. Schläfli, "Sullúso delle linee lungo quali il valore assoluto
fi una funzione é costante [1973],"
Annali Math., Vol. 6, pp. 1-19, 1873-1875. |
| 7. | K. Neumann, Theorie der Bessel'schen Funktionen, Teubner,
Leipzig, 1867. |
| 8. | E. L. Lommel, "Studien über die Bessel'schen Funktionen,"
Teubner, Leipzig, 1868; Math. Ann., Vol. 1, pp. 624-635, 1870. |
| 9. | N. Nilsen, Handbuch der Theorie der Cylinderfunktionen,
Teubner, Leipzig, 1908. |
| 10. | E. A. Coddington and N. Levinson, Theory of
Ordinary Differential Equations [Russian translation], Izd-vo Inostr. Lit-ry,
Moscow, 1958. |
| 11. | E. L. Ince, Ordinary Differential Equations [Russian translation],
Nauchn. Tekhn. Izd-vo Ukr., Kharkov, 1939. |
|
| Received |
24 June 1998 |
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