ABSTRACT An improved model for bending of thin viscoe-lastic plate resting on Winkler foundation is presented. The thin plate is linear viscoelastic and subjected to normal distributed loading, the effect of normal stress along the plate thickness on the deflection and internal forces is taken into account. The basic equations for internal forces and stress distribution are derived based on the general viscoelastic theory under small deformation condition. The reduced equations for elastic case are given as well. It is shown that the proposed model reveals a larger flex-ural rigidity compared to that in classic models, in which the normal stress along the plate thickness is neglected.
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Li, Z. , Yang, T. and Luo, W. (2009) An Improved Model for Bending of Thin Viscoelastic Plate on Elastic Foundation. Natural Science, 1, 120-123. doi: 10.4236/ns.2009.12014.
 Selvadurai, P.S. (1979) Elastic analysis of soil-foundation interaction. Amsterdam: Elsevier.
Kaschiev, M.S. and Mikhajlov, K. (1995) A beam resting on a tensionless Winkler foundation. Computer and Structures, 55, 261-264.
Kim, S.M. and Roesset J.M. (1998) Moving loads on a plate on elastic foundation. Journal of Engineering Me-chanics, 124, 1010-1017.
Mase, G.E. (1960) Behavior of viscoelastic plates in bending. Journal of Engineering Mechanics, 86, 25-39.
Radovskii, S. (1980) Application of the calculation scheme for a layered viscoelastic medium to the estima-tion of the stressed state of highways and airport pave-ments with moving loads. Soviet Applied Mechanics, 15, 940-946.
Pister, K.S. (1961) Viscoelastic plate on a viscoelastic foundation. Journal of Engineering Mechanics, 87, 43-54.
Robertson, S.R. (1971) Solving the problem of forced motion of viscoelastic plates by Valanis’ method with an application to a circular plate. Journal of Sound and Vi-bration, l4, 263-278.
Hewitt, J.S. and Mazumdar, J. (1974) Vibration of vis-coelastic plates under transverse load by the method of constant deflection contours. Journal of Sound and Vi-bration, 33, 319-333.
Sonoda, K., Ishio, T. and Kobayashi, H. (1978) Circular plates on linear viscoelastic foundations. Journal of En-gineering Mechanics, 104, 819-828.
Sonoda, K. and Kobayashi, H. (1980) Rectangular plates on linear viscoelastic foundations. Journal of Engineer-ing Mechanics, 106, 323-338.
Lin, Y.J. (1978) Dynamic response of circular plates resting on viscoelastic half space. Journal of Applied Mechanics, 45, 379-384.
Yang, T.Q., Wang, R. and Yang, Z.W. (1991) Dynamic response of a viscoelastic circular plate on a viscoelastic half space foundation. In: Zyczkowski M (ed.) Creep in Structures, Berlin: Springer-Verlag, 685-692.
Timoshenko, S. and Woinowsky-Krieger, S. (1959) The-ory of Plates and Shells. New York: McGraw-Hill.
Yang, T.Q., Lu, H.B. and Huang, Y.Y. (1987) Quasi-static bending of a thin viscoelastic plate on foun-dations. Journal of Huazhong University of Science and Technology, 15, 1-6 (in Chinese).