Abstract
The analysis of variable thickness plates is much more complicated than that of uniform plates because variable coefficients occur in the governing equations. The purpose of this chapter is to cite some special cases that are amenable to exact analysis, with a brief mention of the applicable methodology.
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Notes
- 1.
See, for example: Y. Xiang, C. M. Wang, Exact vibration and buckling solutions for stepped rectangular plates, Jl. of Sound and Vibration, 250, 2002, 503–517.
- 2.
See, for example: Y. K. Cheung, D. Zhou, The free vibrations of tapered rectangular plates using a new set of beam functions with the Rayleigh–Ritz method , Jl. of Sound and Vibration, 223, 1999, 703–722.
- 3.
H. D. Conway, A Levy-type solution for a rectangular plate of variable thickness, ASME Jl. of Applied Mechanics, 25, 1958, 297–298.
- 4.
E. H. Mansfield, On the analysis of elastic plates of variable thickness, Quarterly Jl. of Mechanics and Applied Mathematics, XV, Part 2, 1962, 167–192.
- 5.
S. P. Timoshenko, S. W. Krieger, Theory of Plates and Shells, McGraw-Hill, 1959, pp. 174–176.
- 6.
K. Akiyama, M. Kuroda, Fundamental frequencies of rectangular plates with linearly varying thickness, Jl. of Sound and Vibration, 205, 1997, 380–384.
- 7.
H. Kobayashi, K. Sonoda, Vibration and buckling of tapered rectangular plates with two opposite edges simply supported and the other two edges elastically restrained against rotation, Jl. of Sound and Vibration, 146, 1991, 323–337.
- 8.
H. Kobayashi, K. Sonoda, Bucklings of rectangular plates with tapered thickness, ASCE Jl. of Structural Engineering, 116, 1990, 1278–1289.
- 9.
M. Saeidifar, S. N. Sadeghi, M. R. Saviz, Analytical solution for the buckling of rectangular plates under uni-axial compression with variable thickness and elasticity modulus in the y-direction, I. Mech. E. Jl. of Mechanical Engineering Science, 224, 2010, 33–41.
- 10.
R. Szilard, Theories and Applications of Plate Analysis, John Wiley and Sons, 2004.
- 11.
See, S. P. Timoshenko, S. W. Krieger, Theory of Plates and Shells, McGraw-Hill, 1959.
- 12.
G. Z. Harris, The normal modes of a circular plate of variable thickness, Quarterly Jl. of Mechanics and Applied Mathematics, 21, 1968, 32–36.
- 13.
T. A. Lenox, H. D. Conway, An exact, closed form, solution for the flexural vibration of a thin annular plate having a parabolic thickness variation, Jl. of Sound and Vibration, 68, 1980, 231–239.
- 14.
See, for example:
J. A. Storch, I. Elishakoff, Apparently first closed-form solutions of inhomogeneous circular plates in 200 years after Chladni, Jl. of Sound and Vibration, 276, 2004, 1108–1114;
I. Elishakoff, G. C. Ruta, Y. Stavsky, A novel formulation leading to closed-form solutions for buckling of circular plates, Acta Mechanica, 185, 2006, 81–88.
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Bhaskar, K., Varadan, T.K. (2021). Variable Thickness Plates. In: Plates. Springer, Cham. https://doi.org/10.1007/978-3-030-69424-1_12
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DOI: https://doi.org/10.1007/978-3-030-69424-1_12
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