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Open AccessArticle

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

by Yuewu Wang 1, Ke Xie 2, Tairan Fu 1,* and Congling Shi 3,*
1
Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Beijing Key Laboratory of CO2 Utilization and Reduction Technology, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
2
Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621900, China
3
Beijing Key Lab of MFPTS, China Academy of Safety Science & Technology, Beijing 100029, China
*
Authors to whom correspondence should be addressed.
Nanomaterials 2019, 9(12), 1690; https://doi.org/10.3390/nano9121690
Received: 22 October 2019 / Revised: 19 November 2019 / Accepted: 22 November 2019 / Published: 26 November 2019
(This article belongs to the Special Issue Multifunctional Polymer-Based Nanocomposite Materials)
A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones. View Full-Text
Keywords: polymer-based nanocomposite; functionally graded material; graphene nanoplatelets; static analysis; free vibration; improved third order shear deformation theory; Chebyshev–Ritz method polymer-based nanocomposite; functionally graded material; graphene nanoplatelets; static analysis; free vibration; improved third order shear deformation theory; Chebyshev–Ritz method
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Wang, Y.; Xie, K.; Fu, T.; Shi, C. Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets. Nanomaterials 2019, 9, 1690.

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