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Warianty tytułu
Języki publikacji
Abstrakty
A comprehensive theoretical study of the free vibration of rotationally restrained rectangular uniform isotropic Mindlin’s plate is presented. The plate mode shape is assumed to be a weighted combination of the product of the Timoshenko beam functions in the either direction, which are previously generated for rotationally constrained boundary conditions. The effect of the uniformly distributed rotational spring constant (modelling the edge) participates in the potential energy of the plate. The Rayleigh-Ritz method has been used to generate the natural frequencies and plate mode shapes for various intermediate boundary conditions, asymptoting to those of the plates with all possible (six) classical boundary conditions. Plates with various thickness ratios have been studied to converge the results to the corresponding Kirchhoff’s frequencies. The eigenvectors from the eigenvalue problem have been scrutinized to establish the beam-wise modal participation from either direction into the final plate mode shape. The square Mindlin’s plate mode shapes have been generated to establish the various types of frequencies; which have been innovatively named and categorized as the (i) single frequencies, (ii) repeated frequencies (identical twins) and (iii) non-repeated frequencies(fraternal twins). Plates with different rectangular aspect ratios have been also analysed to show the deviation in the frequencies and mode shapes from the square plate. Also, their asymptotic behaviour to the corresponding Timoshenko beam at extreme aspect ratios has been established.
Czasopismo
Rocznik
Tom
Strony
129--160
Opis fizyczny
Bibliogr. 24 poz., rys., tab., wykr.
Twórcy
Bibliografia
- 1. Bapat A.V., Venkatramani N., Suryanarayan S., Simulation of classical edge conditions by finite elastic restraints in the vibration analysis of plates, Journal of Sound and Vibration, 120(1): 127–140, 1988.
- 2. Chung J.H., Chung T.Y., Kim K.C., Vibration analysis of orthotropic Mindlin Plates with edges elastically restrained against rotation, Journal of Sound and Vibration, 163(1): 151–163, 1993.
- 3. Courant R., Hilbert D., Methods of mathematical physics, Vol. I, 1st English Ed., Interscience Publishers, Inc., New York, 1966.
- 4. Datta N., Verma Y., Accurate eigenvector-based generation and computational insights of Mindlin’s plate mode shapes for twin frequencies, International Journal of Mechanical Sciences, 123: 64–73, 2017.
- 5. Dawe D.L., Roufaeil O.L., Rayleigh-Ritz vibration analysis of Mindlin plates, Journal of Sound and Vibration, 69(3): 345–359, 1980.
- 6. De Rosa M.A., Lippiello M., Natural vibration frequencies of tapered beams engineering, Engineering Transactions, 57(1):45–66, 2009.
- 7. Gorman D.J., A comprehensive study of the free vibration of rectangular plates resting on symmetrically distributed uniform elastic edge supports, ASME Journal of Applied Mechanics, 56(4): 893–899, 1989.
- 8. Gorman D.J., A general solution for the free vibration of rectangular plates resting on uniform elastic edge supports, Journal of Sound and Vibration, 139(2): 325–335, 1990.
- 9. Huang T.C., The effect of rotary inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions, Journal of Applied Mechanics, 28(4): 579–584, 1961.
- 10. Laura P.A.A., Grossi R.O., Transverse vibration of a rectangular plate elastically restrained against rotation along three edges and free on the fourth edge, Journal of Sound and Vibration, 59(3): 355–368, 1978.
- 11. Laura P.A.A., Romanelli E., Vibrations of rectangular plates elastically restrained against rotation along all edges and subjected to a biaxial state of stress, Journal of Sound and vibration, 37(3): 367–377, 1974.
- 12. Leissa A.W., The free vibration of rectangular plates, Journal of Sound and Vibration, 31(3): 257–293, 1973.
- 13. Leissa A.W., Vibration of plates, NASA SP–160, 1969.
- 14. Liew K.M., Lam K.Y., Chow S.T., Free vibration analysis of rectangular plates using orthogonal plate function, Computers and Structures, 34(1): 79–85, 1990.
- 15. Ma C.C., Hunag C.H., Experimental whole–field interferometry for transverse vibration of plates, Journal of Sound and Vibration, 271(3–5): 493–506, 2004.
- 16. Magrab E.B., Natural frequencies of elastically supported orthotropic rectangular plates, Journal of Acoustical Society of America, 61(1): 79–83, 1977.
- 17. Mindlin R.D., Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates, Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics, 18(1): 31–38, 1951.
- 18. Mindlin R.D., Schacknow A., Deresiewicz H., Flexural vibrations of rectangular plates, Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics, 23(3): 430–436, 1956.
- 19. Saha K.N., Kar R.C., Datta P.K., Free vibration analysis of rectangular Mindlin plates with elastic restraints uniformly distributed along the edges, Journal of Sound and Vibration, 192(4): 885–904, 1996.
- 20. Timoshenko S.P., Vibration problems in engineering, 3rd ed., D. Van Nostrand Company, Inc., New York., pp. 329–331, 1955.
- 21. Traill-Nash R.W., Collar A.R., The effects of shear flexibility and rotatory inertia on the bending vibrations of beams, Quarterly Journal of Mechanics and Applied Mathematics, 6(2): 186–222, 1953.
- 22. Warburton G.B., Edney S.L., Vibrations of rectangular plates with elastically restrained edges, Journal of Sound and Vibration, 95(4): 537–552, 1984.
- 23. Xiang Y., Liew K.M., Kitipornchai S., Vibration analysis of rectangular Mindlin plates resting on elastic edge supports, Journal of Sound and Vibration, 204(1): 1–16, 1997.
- 24. Zhou D., Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method, International Journal of Solids and Structures, 38(32–33): 5565–5580, 2001.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cf44dac2-a040-49a3-a5c5-1b674958cd62