The general formula for calculation of fundamental frequency of axisymmetric vibrations of circular plates with linearly variable thickness

• Autorzy: Jaroszewicz J. , Radziszewski L.
• Języki publikacji: EN

Abstrakty

EN

This work has derived the general formula, sufficiently precise for engineering calculations of base frequency of axisymmetric free vibrations of uniform, circular diaphragm type plates clamped at the edge with linearly variable thickness. To solve the boundary problem, the Cauchy’s function method and characteristic series have been applied. The above formula has been derived on the basis of Dunkerley’s formula which is based on the first major term of the characteristic series and results in the simplest, lower bound estimator. The analysis of the formula shows that the base frequency coefficient for diaphragm plates clamped at the edge depends to only a small extent on the Poisson’s ratio, and therefore it may be averaged in the case of construction materials. Comparison of the calculations results of the simplest lower bound estimators for the base frequency obtained by using proposed method, with the results known from the literature as precise solutions, including Conway method, confirmed the high accuracy of the proposed method.

Słowa kluczowe

EN

circular plates; variable thickness; boundary value problem; Cauchy function method; simple estimator of fundamental frequency

• Wydawca: Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego w Olsztynie
• Czasopismo: Technical Sciences / University of Warmia and Mazury in Olsztyn
• Rocznik: 2016
• Tom: nr 19(4)
• Strony: 401--410
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Jaroszewicz J.

• Katedra Zarządzania Produkcją, Politechnika Białostocka, ul. Ojca Tarasiuka 2, 16-001 Kleosin

autor

Radziszewski L.

• Departments of Mechanics Kielce University of Technology

Bibliografia

• BERNSTEIN S.A., KIEROPIAN K.K. 1960. Opredelenije cˇastot kolebanij sterzˇnevych system metodom spektralnoi funkcii. Gosstroiizdat, Moskva, p. 281.
• CONWAY H.D. 1958a. Some special solutions for the flexural vibrations of discs of varying thickness. Ing. Arch., 26(6): 408-410.
• CONWAY H.D. 1958b. An analogy between the flexural vibrations of a cone and a disc of linearly varying thickness. Z. Angew. Math. Mech., 37(9-10): 406-407.
• DOMORADZKI M., JAROSZEWICZ J., ZORYJ L. 2005. Anslysis of influence of elastisity constants and material density on base frequency of axi-symmetrical vibrations with variable thickness plates. Journal of Theoretical and Applied Mechanics, 43(4): 763-775.
• JAROSZEWICZ J., MISIUKIEWICZ M., PUCHALSKI W. 2008. Limitations in application of basic frequency simplest lower estimators in investigation of natural vibrations of circular plates with variable thickness and clamped edges. Journal of Theoretical and Applied Mechanics, 46(1): 109-212.
• JAROSZEWICZ J., ZORYJ L. 2005. Metody analizy drgań osiowosymetrycznych płyt kołowych z zastosowaniem metody funkcji wpływu Cauche’go. Rozprawy Naukowe Politechniki Białostockiej, 124: 120.
• JAROSZEWICZ J., ZORYJ L. 2006. The method of partial discretization in free vibration problems of circular plates with variable distribution of parameters. International Applied Mechanics, 42(3): 364-373.
• JAROSZEWICZ J., ZORYJ L., KATUNIN A. 2006. Influence of additional mass rings on frequencies of axi-symmetrical vibrations of linear variable thickness clamped circular plates. Journal of Theoretical and Applied Mechanics, 44(4): 867-880.
• KOVALENKO A.D. 1959. Kruglyje plastiny peremenntoj tolshchiny. Gosudarstvennoje Izdanie FizikoMatematicheskoj Literatury, Moskva, p. 294.
• HONDKIEWIČ W.S. 1964. Sobstviennyje kolebanija plastin i obolochek Kiev. Nukowa Dumka, p. 288.
• VASYLENKO N.V. 1992. Teoriya kolebanij, Vyshcha Shkola, Kiev, p. 429.
• VASYLENKO M.V., ALEKSEJCHUK O.M. 2004. Teoryja kolyvań i stijkosti ruhu, Vyshcha Shkola, Kiev, p. 525.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.