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Appl. Sci. 2019, 9(8), 1580; https://doi.org/10.3390/app9081580

Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations

1
Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-51167, Iran
2
Department of Innovation Engineering, University of Salento, 73100 Lecce, Italy
3
Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA
*
Author to whom correspondence should be addressed.
Received: 9 March 2019 / Revised: 10 April 2019 / Accepted: 11 April 2019 / Published: 16 April 2019
(This article belongs to the Special Issue Recent Advances in Non-Local Modelling of Nano-Structures)
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Abstract

This paper presents a free vibration analysis of functionally graded (FG) polymer composite curved nanobeams reinforced with graphene nanoplatelets resting on a Pasternak foundation. The size-dependent governing equations of motion are derived by applying the Hamilton’s principle and the differential law consequent (but not equivalent) to Eringen’s strain-driven nonlocal integral elasticity model equipped with the special bi-exponential averaging kernel. The displacement field of the problem is here described in polar coordinates, according to the first order shear deformation theory. A large parametric investigation is performed, which includes different FG patterns, different boundary conditions, but also different geometrical parameters, number of layers, weight fractions, and Pasternak parameters. View Full-Text
Keywords: composite curved nanobeam; first-order shear deformation theory; graphene nanoplatelet; Pasternak foundation; size-dependent vibration composite curved nanobeam; first-order shear deformation theory; graphene nanoplatelet; Pasternak foundation; size-dependent vibration
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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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Arefi, M.; Bidgoli, E. .-R.; Dimitri, R.; Tornabene, F.; Reddy, J.N. Size-Dependent Free Vibrations of FG Polymer Composite Curved Nanobeams Reinforced with Graphene Nanoplatelets Resting on Pasternak Foundations. Appl. Sci. 2019, 9, 1580.

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