VIBRATION OF THE PLATE DE FORME ELLIPTIQUE

Authors

  • О. M. Чемерис NTUU KPI, Ukraine

DOI:

https://doi.org/10.20535/2305-9001.2014.70.28062

Keywords:

elliptic, jammed and hinged plate, frequenci

Abstract

Whole elliptic form a plate on an external contour is jammed or pin-ended. In this work the smallest eigenfrequencies at the symmetric vibrations of such plate are determined.

The calculations of frequency parameter on different approximate formulas are conducted with the purpose of determination of their ranges of definition. All exhibited formulas for a frequency parameter at the values of eccentricity of ellipse approximately less or equal 0.5 coincide. At the increase of eccentricity the results of calculation substantially diverge and needed further theoretical experimental researches for establishment of law of change of frequency parameter depending on an eccentricity. For a whole elliptic pin-ended plate is developed the algorithm of determination of frequency parameter. On the basis of Mathieu function a frequency equation was composed and his smallest roots was found. The smallest frequencies of symmetric vibrations were calculated. As well as in case of the jammed plate frequency of vibrations increase with the increase of eccentricity

References

1. Strett M.D. Fynktii Lame, Mathieu I rodstvinie im v phisike I texnike. Moskow. Hostexisdat .1935. 159-164p.

Mac Lachlan, Teoria I prilogenia phynkti Mathieu. I.L., 1954.

Mathieu E., Memorie sur le movement vibratorie d’une membrane de form elliptique, J. de math, pures et appliqués (Liouville), 1868. v. 13. p. 137.

Collatz l., Eigenwertaufgaben mit technishen Anwendungen, Akad. Verlad. Lpz. 1949

Shibaoka Y., On the transverse vibration of an elliptic plate with clamped edges. J.Phys. Sos. Japan, 1956, 11, no 7, p. 797.

Gontkevich V.S. Sobstvennye kolebanija plastinok. Spravochnoe posobie [Frequencies of eigentones plates. Certificate manual]. Kyiv: Naukova dumka, 1964, 287p.

Spravochnik po dinamike sooruzhenij [Reference book on the dynamics of buildings]. Pod red. Koreneva B.G, Rabinovicha. I.M. M: Strojizdat, 1972, 511p

Downloads

Published

2014-10-13

Issue

No. 70 (2014)

Section

Статті

License

The authors reserve the right to authorship of the work and pass the journal right of first publication of this work is licensed under a Creative Commons Attribution License, which allows others to freely distribute the work published with reference to the authors of the original work and the first publication of this magazine.