Abstract
A pure analytic solution of the axisymmetric large amplitude free vibration of thin annular plates is presented in this paper: By using the modified iteration method, we derive an analytic relation for the amplitudes vs. frequencies of vibrations. The present paper shows the great potentiality of this method to tackle the large amplitude vibration problems of plates.
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Nayfeh, A. H. and D. T. Mook,Nonlinear Oscillations, John Wiley & Sons, Inc., New York (1979).
Sandman, B. E. and C. L. Huang, Finite amplitude oscillations of a thin elastic annulus,Dev. Mech.,6 (1971), 921–934.
Huang, C. L., Nonlinear oscillations of an annulus with variable thickness,Dev. Theor. Appl. Mech.,7 (1974), 271–284.
Huang, C. L. and H. K. Woo, et al., Nonlinear flexural oscillations of a partially tapered annular plate,Inter. J. Non-Linear Mech.,11 (1976), 89–97.
Reddy, J. N. and C. L. Huang, Large amplitude free vibrations of annular plates of variable thickness,J. Sound Vib.,79 (1981), 387–396.
Liu, R. H., Nonlinear bending of circular sandwich plates,Appl. Math. and Mech.,2, 2 (1981), 189–208.
Liu, R. H., Nonlinear thermal stability of bimetallic shallow shells of revolution,Inter. J. Non-Linear Mech.,18 (1983), 409–429.
Liu, R. H. and D. Li, On the nonlinear stability of a truncated shallow spherical shell under uniformly distributed load,Appl. Math. and Mech.,9, 3 (1988), 227–240.
Li, D. and R. H. Liu, Nonlinear free vibration of thin circular plates,Adv. Appl. Math. Mech. China, Edited by Chien Wei-zang,3 (1989).
Li, D. and R. H. Liu, Application of the modified iteration method to nonlinear vibration of corrugated circular plates,Appl. Math. and Mech.,11, 1 (1990), 13–22.
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Communicated by Liu Ren-huai
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Dong, L. Large amplitude vibration of thin annular plates. Appl Math Mech 12, 583–593 (1991). https://doi.org/10.1007/BF02015572
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DOI: https://doi.org/10.1007/BF02015572