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Free vibration analysis of isotropic rectangular plates on Winkler foundation using differential transform method

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A differential transform method (DTM) is used to analyze free transverse vibrations of isotropic rectangular plates resting on a Winkler foundation. Two opposite edges of the plates are assumed to be simply supported. This semi-numerical-analytical technique converts the governing differential equation and boundary conditions into algebraic equations. Characteristic equations are obtained for three combinations of clamped, simply supported and free edge conditions on the other two edges, keeping one of them to be simply supported. Numerical results show the robustness and fast convergence of the method. Correctness of the results is shown by comparing with those obtained using other methods.
Rocznik
Strony
589--597
Opis fizyczny
Bibliogr. 14 poz., tab.
Twórcy
autor
  • Department of Mathematics M.K. Government Degree College Ninowa Farrukhabad-209 602, Uttar Pradesh, India
Bibliografia
  • Arikoglu A. and Ozcol I. (2005): Solution of boundary value problems for integro-differential equation by usingdifferential transform method. - Appl. Math. Comp., vol.168, pp.1145-1158.
  • Attarnejad R., Shabha A. and Semnani S.J. (2010): Application of differential transform in free vibration analysis ofTimoshenko beams resting on two- parameter elastic foundation. - The Arabian J. Sci. Eng., vol.35(2B), pp.125-132.
  • Bambill D.V., Rossit C.A., Laurra P.A.A. and Rossit R.E. (2000): Transverse vibrations of an orthotropic rectangularplate of linearly varying thickness and with a free edge. - J. Sound Vib., vol.235(3), pp.530-538.
  • Bhat R.B., Laura P.A.A., Gutierrez R.G., Cortinez V.H. and Sanzi V.H. (1990): Numerical experiment on thedetermination of natural frequencies of transverse vibrations of rectangular plates of non-uniform thickness. - J. Sound Vib., vol.138, pp.205-219.
  • Chen J.T., Chen I.L., Lee Y.T. and Yeh Y.T. (2004): A meshless method for free vibration analysis of circular andrectangular clamped plates using radial basis function. - Eng. Analysis with Boundary Elements, vol.28, No.5, pp.535-545.
  • Gorman D.J. (2000): Free vibration analysis of completely free rectangular plates by the Superposition-Galerkinmethod. - J. Sound Vib., vol.237(5), pp.901-914.
  • Kacar A., Tan H.T. and Kaya M.O. (2011): Free vibration analysis of beams on variable elastic foundation by using thedifferential transform method. - Mathematical Compu. Applications, vol.16(3), pp.773-783.
  • Malik M. and Allali M. (2000): Characteristic equations of rectangular plates by differential transform method. - J. Sound Vib., vol.233(2), pp.359-366.
  • Omer C., Armagan K. and Cigdem D. (2010): Discrete singular convolution approach for buckling analysis ofrectangular Kirchoff plates subjected to compressive loads on two opposite edges. - Adv. Eng. Software, vol.41, pp.557-560.
  • Venkateswara R.G., Prakash R.B. and Raju I.S. (1974): Vibrations of inhomogeneous thin plates using a high precisiontriangular element. - J. Sound Vib., vol.34(3), pp.444-445.
  • Wang X., Gan L. and Wang Y. (2006): A differential quadrature analysis of vibration and buckling of an SS-C-SS-Crectangular plate loaded by linearly varying in-plane stress. - J. Sound Vib., vol.298, pp.420-431.
  • Yajuvindra Kumar and Lal R. (2011): Vibrations of nonhomogeneous orthotropic rectangular plates with bilinearthickness variation resting on Winkler foundation. - Meccanica, DOI:10.1007/s11012-011-9459-4.
  • Yalcin H.S., Arikoglu A. and Ozcol I. (2000): Free vibration analysis of circular plates by differential transformmethod. - Appl. Math. Comp., vol.212, pp.377-386.
  • Zhou J.K. (1986): Differential transformation and its application for electrical circuits (in Chinese). - Wuhan, P.R. China: Huazhong University Press.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-55990bb1-b142-4cd3-94ce-0d21f43b5549
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