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A nth-order shear deformation theory for the free vibration analysis on the isotropic plates

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Abstract

In the present paper, a nth-order shear deformation theory is used to perform the free vibration analysis of the isotropic plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third order theory can be considered as a special case of present nth-order theory (n=3). The governing equations and boundary conditions are derived by the principle of virtual work. The governing differential equations of the isotropic plates are solved by the meshless radial point collocation method based on the thin plate spline radial basis function. The effectiveness of the present theory is demonstrated by applying it to free vibration problem of the square and circular isotropic plate.

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Authors and Affiliations

  1. Liaoning Key Laboratory of General Aviation, Shenyang Aerospace University, No. 37 Daoyi South Avenue, Shenyang, Liaoning, 110136, People’s Republic of China

    Song Xiang & Gui-wen Kang

  2. Technical Center, Avic Shenyang Liming Aero-Engine (Group) Corporation Ltd., Shenyang, Liaoning, 110043, People’s Republic of China

    Bin Xing

Authors
  1. Song Xiang
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  2. Gui-wen Kang
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  3. Bin Xing
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Correspondence to Song Xiang.

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Xiang, S., Kang, Gw. & Xing, B. A nth-order shear deformation theory for the free vibration analysis on the isotropic plates. Meccanica 47, 1913–1921 (2012). https://doi.org/10.1007/s11012-012-9563-0

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