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Bending and vibration analysis of generalized gradient elastic plates

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Abstract

The governing equations of motion of generalized gradient Kirchhoff and Mindlin plates are derived on the basis of the generalized gradient elasticity with both stress and strain gradient parameters. The present plate models incorporate two material length scale parameters that can capture the size effect. The proposed models are capable of dealing with size-dependent plates at nanoscale dimension with complex geometries and boundary conditions with the help of Hamilton’s principle. The static bending and free vibration of a rectangular simply supported all around generalized gradient Kirchhoff and Mindlin plates are solved analytically using Navier’s solution. A circular gradient elastic plate, clamped all around, is also analyzed under linear static loading. Finally, the present solutions are discussed in relation to their corresponding conventional ones.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Xiao-Jian Xu, Zi-Chen Deng, Jun-Miao Meng & Kai Zhang

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Zi-Chen Deng

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  1. Xiao-Jian Xu
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  2. Zi-Chen Deng
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  3. Jun-Miao Meng
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  4. Kai Zhang
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Correspondence to Zi-Chen Deng.

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Xu, XJ., Deng, ZC., Meng, JM. et al. Bending and vibration analysis of generalized gradient elastic plates. Acta Mech 225, 3463–3482 (2014). https://doi.org/10.1007/s00707-014-1142-0

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  • DOI: https://doi.org/10.1007/s00707-014-1142-0

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