Natural frequencies of axisymmetric vibrations of thin hyperbolic circular plates with clamped edges

• Autorzy: Jaroszewicz J.

Identyfikatory

DOI

10.1515/ijame-2017-0028

• Języki publikacji: EN

Abstrakty

EN

A free vibration analysis of homogeneous and isotropic circular thin plates with nonlinear thickness variation and clamped edges is considered. The limited independent solutions of differential Euler equation were expanded in the power series based on the properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations.

Słowa kluczowe

EN

circular plates; power series; clamped edge

PL

drgania jednorodne; równanie Eulera; częstotliwość

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2017
• Tom: Vol. 22, no. 2
• Strony: 451--457
• Opis fizyczny: Bibliogr. 15 poz., tab., wykr.

Twórcy

autor

Jaroszewicz J.

• Faculty of Management Bialystok University of Technology 2 Ojca Stefana Tarasiuka St., 16-001 Kleosin, POLAND

Bibliografia

• [1] Leissa A.W. (1969): Vibration of Plates. – Washington.
• [2] Conway H.D. (1957): An analogy between the flexural vibrations of a cone and a disc of linearly varying thickness. – Journal of Applied Mathematics and Mechanics, vol.37, No.9, pp.406-407.
• [3] Conway H.D. (1958): Some special solutions for the flexural vibrations of discs of varying thickness. – Ingenieur-Archiv, vol.26, No.6, pp.408-410.
• [4] Jain R.K., Prasad C. and Soni S.R. (1972): Axisymmetric vibrations of circular plates of linearly varying thickness. – ZAMP, vol.23, pp.941-947.
• [5] Wang J. (1997): General power series solution of the vibration of classical circular plates with variable thickness. – Journal of Sound and Vibration, vol.202, pp.593-599.
• [6] Wu T.Y. and Liu G.R. (2001): Free vibration analysis of circular plates with variable thickness by the generalized differential quadrate rule. – International Journal of Solids and Structures, vol.38, pp.7967-7980.
• [7] Wu T.Y. and Liu G.R. (2002): Free vibration analysis of circular plates using generalized differential quadrature rule. – Computer Methods in Applied Mechanics and Engineering, vol.191, pp.5365-5380.
• [8] Jaroszewicz J. and Zoryj L. (2006): The method of partial discretization in free vibration problems of circular plates with variable distribution of parameters. – International Applied Mechanics, vol.42, pp.364-373.
• [9] Zhou Z.H., Wong K.W., Xu X.S. and Leung A.Y.T. (2011): Natural vibration of circular and annular plates by Hamiltonian Approach. – Journal of Sound and Vibration, vol.330, No.5, pp.1005-1017.
• [10] Duan G., Wang X. and Jin Ch. (2014): Free vibration analysis of circular thin plates with stepped thickness by the DSC element method. – Thin-Walled Structures, vol.85, pp.25-33.
• [11] Żur K.K. (2015): Green’s function in frequency analysis of circular thin plates of variable thickness. – Journal of Theoretical and Applied Mechanics, vol.53, No.4, pp.873-884.
• [12] Żur K.K. (2016a): Green’s function approach to frequency analysis of thin circular plates. – Bulletin of the Polish Academy of Sciences – Technical Sciences, vol.64, No.1, pp.181-188.
• [13] Żur K.K. (2016b): Green’s function in frequency analysis of thin annular plates of nonlinear thickness variation. – Applied Mathematical Modelling, vol.40, pp.5-6, pp.3601-3619.
• [14] Jaroszewicz J. and Zoryj L. (2005): Method of free aximmetric vibration analysis of circular plates via method of influece Cauchy function – Rozprawy Naukowe Politechniki Białostockiej Nr 124, Białystok, pp.120.
• [15] Jaroszewicz J., Misiukiewicz M. and 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, No.1, pp.109-121.