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УДК 539.3

 

Chemeris O.

National Technical University of Ukraine «Kyiv Polytechnic Institute», Kyiv, Ukraine ( This e-mail address is being protected from spambots. You need JavaScript enabled to view it )

 

VIBRATION OF THE CIRCULAR ANNULAR PLATE WITH

 

Circular annual plate hinged fixed on an internal circuit which is jammed and free. For the decision of task the Bessel function of different sort of a zero and first order are used . For every form of vibrations, n = 0 , 1, 2 worked out frequency equations and equalization for determination of position of nodal circumferences. The results of calculations of eigenfrequencies are conducted in the case when number of nodal diameters ( n = 0,1..2 ), and number of nodal circumferences (s=0, 1, 2). The results of calculations are conducted on position-finding nodal rings in the case when number of nodal diameters ( n = 0,1..2 ), and the number of nodal circumferences (s=0, 1, 2, 3 . The work can be used for determination of eigenfrequencies of machines and devices.

 

References
1. Saharov I.E. Chastoti sobstvennyh kolebanij kol'cevyh plastinok [Frequencies of eigentones of circular plates]. Izvestija AN SSSR, OTN no 5, 1957.
2. Saharov I.E. Dinamicheskie zhjostkosti v teorii osesimmetrichnyh kolebanij kruglyh i kolcevyh plastinok, [Dynamic inflexibilities are in the theory of axisymmetrical vibrations of round and circular plates]. Izvestija AN SSSR, Mehanika, no 5, 1959.
3. Gontkevich V.S. Sobstvennye kolebanija plastinok. Spravochnoe posobie [Frequencies of eigentones plates. Certificate manual] Kyiv: Naukova dumka, 1964, 287p.
4. Spravochnik po dinamike sooruzhenij [Reference book on the dynamics of buildings]. Pod red. B.G.Koreneva, I.M.Rabinovicha. Moscow: Strojizdat, 1972, 511p.
5. Vajnberg D.V. Spravochnik po prpochnosti,ustojchivosti i kolebanijam plastin [Reference book on durability, stability and vibrations of plates]. Kyiv: Budіvelnik, 1973, 487p.
6. Chemeris O Коливання круглих шарнірно закріплених кільцевих пластин. Вісник НТУУ “КПІ”, Серія «Машинобудування», No 62, 2011, С183-186
7. Chemeris O. Коливання кільцевої пластинки з ковзною опорою. Вісник НТУУ “КПІ”, Серія «Машинобудування», No 64, 2012.
8. Korenev V.G. Nekotorye zadachi teorii uprugosti i teploprovodnosti, reshaemye v besselevyh funkcijah [Some tasks of theory of resiliency and heat conductivity Some tasks of theory of resiliency and heat conductivity which are solved Bessel functions]. Moscow: Fizmatgiz, 1969, 358p.

 

 

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