THE AXISYMMETRIC DYNAMICS OF ISOTROPIC CIRCULAR PLATES WITH VARIABLE THICKNESS UNDER THE EFFECT OF LARGE AMPLITUDES
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Abstract
This paper presents a study of the geometrically non-linear vibrations of clamped circular plates with variable thickness by taking the effect of large amplitude motion. The maximum thickness is considered to be at the plate center and it is taken to be twice the value of thickness at the edge. The problem is solved by the numerical iteration procedure to obtain the results of vibration amplitudes up to twice the maximum plate thickness. The results are presented for the first two modes of vibration. The obtained results indicate
that increasing the ratio of thickness has the effect of increasing the nonlinear frequency and modify the corresponding mode shape.
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References
C.F. Liu, G.T. Chen, “Geometrically nonlinear Axisymmetric Vibrations of Polar Orthotropic Circular Plates”, International Journal of Mechanical Science, 38, 3, 1996, pp. 1715-1726.
C.F. Liu, G.T. Chen, “Geometrically nonlinear Axisymmetric Vibrations of Polar Orthotropic Circular Plates”, International Journal of Mechanical Science, 38, 3, 1996, pp.1715-1726.
C.L.D. Huang, I.M. Al-Khattat, “Finite Amplitude Vibrations of a Circular Plate”, International Journal of nonlinear Mechanics, 12, 1977, pp. 297-306.
L. Azrar, R. Benamar, R.G. White, “A Semi-Analytical Approach to the nonlinear Dynamic Response Problem of S-S C-C Beams at Large Vibration Amplitudes. Part I: General Theory and Application to the Single Mode Approach to free and Forced Vibration Analysis”, Journal of Sound &Vibration, 224, 2, 1999, pp. 183-207.
L.C. Wellford, G.M. Dib, W. Mindle, “Free and Steady-State Vibration of nonlinear Structures using a Finite Element nonlinear Eigenvalue Technique”, Earthquake Engineering and Structural Dynamics, 8, 1980, pp. 97-115.
M. El Kadiri, R. Benamar, R.G. White, “Improvement of the Semi-Analytical Method for Determining the Geometrically non-linear Response of Thin Straight Structures. Part I: Application to Clamped-Clamped and Simply Supported_ Clamped Beams”, Journal of Sound &Vibration, 249, 2002, pp. 263-205.
M. Haterbouch, R, Benamar, “The Effects of Large Vibration Amplitudes on the Axisymmetric Mode Shapes and Natural Frequencies of Clamped Thin Isotropic Circular Plates. Part I: Iterative and Explicit Analytical Solution for nonlinear Transverse Vibrations”, Journal of Sound &Vibration, 265, 2003, pp. 123-154.
M. Haterbouch, R, Benamar, “The Effects of Large Vibration Amplitudes on the Axisymmetric Mode Shapes and Natural Frequencies of Clamped Thin Isotropic Circular Plates. Part II: Iterative and Explicit Analytical Solution for nonlinear Transverse Vibrations”, Journal of Sound &Vibration, 277, 2004, pp. 1-30.
R. Benamar, “Non-linear Dynamic Behaviour of Fully Clamped Beams and Rectangular isotropic Laminated Plates”, Ph.D. Thesis, Institute of Sound and Vibration Research, 1990
R. Benamar, M.M.K. Bennouna, R.G. White, “The effects of Large Vibration Amplitudes on the Mode Shapes and Natural Frequencies of Thin Elastic Structures. Part I: Simply Supported and Clamped-Clamped Beams”, Journal of Sound &Vibration, 194, 1991, pp. 179-195.
S. Huang, “Nonlinear Vibration of a Hinged Orthotropic Circular Plate with a Concentric Rigid Mass”, Journal of Sound &Vibration, 241, 5, 1998, 873-883.
S. Timoshinko, S. Woinowsky-Krieger, “Theory of Plates and Shells”, 2nd Edd., Mcgraw-Hill, New York, 1959.
T.W. Lee, P.T. Blotter, D.H.Y. Yen, “On the nonlinear Vibrations of a Clamped Circular Plate” Developments in Mechanics, 6, 1971, pp. 907-921.