 | | 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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| S.A. Kuliev, "Vibrations of a Polygonal Plate Weakened by a Circular Hole with Two Rectilinear Cuts," Mech. Solids. 48 (6), 682-696 (2013) |
| Year |
2013 |
Volume |
48 |
Number |
6 |
Pages |
682-696 |
| DOI |
10.3103/S0025654413060113 |
| Title |
Vibrations of a Polygonal Plate Weakened by a Circular Hole with Two Rectilinear Cuts |
| Author(s) |
S.A. Kuliev (Azerbaijan Architecture-Construction University, Ayny Sultanovoy 5, Baku, AZ 1000 Azerbaijan, gulin@bp.com, nigar_sabir@yahoo.com) |
| Abstract |
We consider free bending vibrations of a finite isotropic plate bounded on the outside by a polygon L2 (e.g., a square, an ellipse, a circle, etc.) and on the inside by the contour L1 formed by the circle of radius r with two rectilinear cuts located symmetrically on the axis Ox. The plate is rigidly clamped along the entire outer contour L2, and the inner contour L1 is free.
We reduce the solution of the plate vibration problem to the integration of a fourth-order differential equation [2, 4, 5].
The method used in this paper is well known in the literature [2, 4, 5, 11] for simple simply connected domains, but the case under study (a doubly connected domain with cuts) has not yet been considered, because no mapping functions z=λ(ξ) have been known for complicated domains (doubly connected domain with cuts). The author [6-8] is the first in the scientific world to find such mapping functions. The obtained theoretic solution is illustrated by numerical examples. |
| Keywords |
vibration, rectilinear cut, vibration frequency, mapping function |
| References |
| 1. | Yu. A. Amenzade,
Theory of Elasticity
(Vysshaya Shkola, Moscow, 1976)
[in Russian]. |
| 2. | I. M. Babakov,
Theory of Oscillations
(Nauka, Moscow, 1968)
[in Russian]. |
| 3. | N. I. Muskhelishvili,
Several Fundamental Problems of Mathematical Theory of Elasticity
(Nauka, Moscow, 1966)
[in Russian]. |
| 4. | V. G. Zhitnyaya and A. S. Kosmodaminskii,
"Free Bending Oscillations of a Finite Plate with Rigidly Fixed Edge,"
in Theoretical Applied Mechanics, No. 15
(Done, Kiev, 1984), pp. 80-87
[in Russian]. |
| 5. | A. I. Aleksandrovich,
"Study of Equations of Dynamic Problems of Elasticity
by Holomorphic Expansion,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 1, 78-82 (1979)
[Mech. Solids (Engl. Transl.)]. |
| 6. | S. A. Kuliev,
Conformally-Mapping Functions of Complicated Domains
(Azerneshr, Baku, 2004). |
| 7. | S. A. Kuliev,
Two-Dimensional Problems of Theory of Elasticity
(Stroiizdat, Moscow, 1991)
[in Russian]. |
| 8. | S. A. Kuliev,
"Bending of a Polygonal Plate with a Central Circular Hole
and Two Rectilinear Cuts of Different Length,"
Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela,
No. 6, 173-179 (1990)
[Mech. Solids (Engl. Transl.)]. |
| 9. | A. N. Guz', V. D. Kubenko, and M. A. Cherevko,
Diffraction of Elastic Waves
(Kiev, Naukova Dumka, 1978)
[in Russian]. |
| 10. | D. I. Sherman,
"To Solution of Plane Static Problem of Elasticity for Given External Forces,"
Dokl. Akad. Nauk SSSR
28 (1), 25-28 (1940)
[Sov. Phys. Dokl. (Engl. Transl.)]. |
| 11. | D. I. Sherman,
"On Certain Problems of Theory of Stationary Oscillations,"
Izv. Akad. Nauk SSSR Ser. Mat.,
No. 9, p. 7 (1945)
[Math. USSR-Izv. (Engl. Transl.)]. |
| 12. | D. I. Sherman,
"On Steady-State Elastic Oscillations for Given Displacements on the Medium Boundary,"
Prikl. Mat. Mekh.
17 (10), (1946)
[J. Appl. Math. Mech. (Engl. Transl.)]. |
| 13. | D. I. Sherman,
"On Reduction of Some Problems of Theory of Stationary Oscillations
to the Fredholm Integral Equation,"
Izv. Akad. Armyan. SSR Ser. Mat.
XVI (4), 41-63 (1963)
[Soviet J. Contemporary Math. Anal. (Engl. Transl.)]. |
|
| Received |
08 February 2012 |
| Link to Fulltext |
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