On the Three-Dimensional Vibration Analysis of Rectangular Plates
This paper is concerned with the free vibration analysis of simply supported rectangular plates with any thickness. The analysis is based on the linear, small-strain, three-dimensional elasticity theory. It aims to raise the quality of investigation beyond that provided by the approximate two- and three-dimensional plate theories, by resorting to an exact three-dimensional analysis. The proposed technique yields the full vibration spectrum of natural frequencies and mode shapes. The vibration response due to the variations of thickness is investigated. Frequency parameters and three-dimensional deformed mode shapes are presented in vivid graphical forms. Finally, some new numerical results are given, which may serve as benchmark solutions for future research on the aforementioned problem and for validating approximate three-dimensional theories and new computational techniques in the future.
KeywordsMode Shape Free Vibration Thick Plate Plate Theory Frequency Parameter
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- C. Gentilini, A. Mazza, and E. Viola. Analisi dinamica esatta delle piastre spesse. Technical Report 84, DISTART, University of Bologna, 2002.Google Scholar
- C. Gentilini and E. Viola. Risposta in termini di tensione nell’analisi dinamica di piastre. Technical Report 85, DISTART, University of Bologna, 2002.Google Scholar
- A.W. Leissa and Z. Zhang. On the three-dimensional vibrations of a cantilevered rect angular parallelepiped. Journal of Acoustic of America73:2013–2021, 1983. Google Scholar
- R.D. Mindlin. Influence of rotatory inertia and shear on flexural motion of isotropic elastic plates. ASME Journal of Applied Mechanics, 73: 31–38, 1951.Google Scholar
- R.D. Mindlin, A. Schacknow, and H. Deresiewickz. Flexural vibrations of rectangular plates. ASME Journal of Applied Mechanics, 18: 430–436, 1956.Google Scholar
- J. Nanni. Das eulersche knickproblem unter berucksichtigung der querkrafte. Zeitschrift fur Angewandte Mathematik und Phisysik, 22, 1971.Google Scholar
- Y.S. Uflyand. The propagation of waves in the transverse vibrations of bars and plates. Akademia Nauk SSSR, Prikladnaya Matematika i Mekhanika, 12, 1948.Google Scholar
- E. Viola and C. Gentilini. Influenza dello spessore sul comportamento dinamico delle piastre. Technical Report 86, DISTART, University of Bologna, 2002.Google Scholar
- J.M. Whitney and C.T. Sun. A higher-order theory for extensional motion of laminated composites. Journal of Sound and Vibration, 30 (1), 1973.Google Scholar