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Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches

Institute of Machine Design, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
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Appl. Sci. 2019, 9(7), 1409; https://doi.org/10.3390/app9071409
Received: 27 February 2019 / Revised: 26 March 2019 / Accepted: 1 April 2019 / Published: 3 April 2019
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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Abstract

The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations. View Full-Text
Keywords: nonlocal stress theory; nonlocal strain theory; buckling; free vibrations; nanoplates; higher order shear deformation theories nonlocal stress theory; nonlocal strain theory; buckling; free vibrations; nanoplates; higher order shear deformation theories
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chwał, M.; Muc, A. Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches. Appl. Sci. 2019, 9, 1409.

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