Limitation of Cauchy Function Method in Analysis of Estimators of Frequency and Form of Natural Vibrations of Circular Plate with Variable Thickness and Clamped Edges

• Autorzy: Jaroszewicz J. , Żur K.
• Języki publikacji: EN

Abstrakty

EN

In this paper the Berstein-Kieropian double estimators of basic natural frequency of circular plate with power variable thickness along the radius and clamped edges in diaphragm form were analyzed in a theoretical approach. The approximate solution of boundary problem of transversal vibration by means of Cauchy function and characteristic series method has been applied for chosen values of power indicator of variable thickness and material Poisson’s ratio has been chosen which led to exact form solutions. Particular attention has been given to a singularity arising from the uncertainty of estimates of Bernstein-Kieropian. Improving this method has been obtained the general form of Cauchy function for arbitrary values of and , which are physically justified. Therefore, the aim of the paper was to explore the reason why for a plate above a certain value = 3.97 exact solution, which Conway couldn’t receive (Conway, 1958a, b)

Słowa kluczowe

EN

vibration; circular plate; boundary value problem; Cauchy function; Bernstein-Kieropian’s estimators

PL

drgania; model płaskiej struktury; zagadnienia brzegowe; estymatory Bernsteina-Kieropiana

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2012
• Tom: Vol. 6, no. 2
• Strony: 53--57
• Opis fizyczny: Bibliogr. 14 poz., Rys.

Twórcy

autor

Jaroszewicz J.

autor

Żur K.

• Faculty of Management, Bialystok University of Technology, ul. Ojca Tarasiuk 2, 16-001 Kleosin, Poland,

Bibliografia

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• 3. Conway H.D. (1958a), Some special solutions for the flexural vibrations of discs of varying thickness, Ing. Arch., 26, 6, 408-410.
• 4. 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.
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• 7. Jaroszewicz J., Misiukiewicz M., Puchalski W. (2008), Limitations in application of basic frequency simplest lower estimators in investigation of natural vibrations circular plates with variable thickness and clamped edges, Journal of Theoretical and Applied Mechanics, Vol. 46, nr 1, 109-121.
• 8. Jaroszewicz J., Zoryj L. (2000), Investigation of the effect of axial loads on the transverse vibrations of a vertical cantilever with variables parameters, International Applied Mechanics, Volume 36, Number 9, 1242-1251.
• 9. Jaroszewicz J., Zoryj L. (2005), Methods of analysis natural vibration of axi-symmetrical plates using Cauchy function, Białystok.
• 10. 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.
• 11. 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.
• 12. Kovalenko A.D. (1959), Kruglyje plastiny peremenntoj tolshchiny, Gosudarstvennoje Izdanie Fiziko-Matematicheskoj Literatury, Moskva.
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• 14. Woźniak C. (2001), Mechanics of elasticity plates and shells, Polish Academy of Sciences, PWN, Warsaw.