Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model

Yunhe Zou () and Yaser Kiani ()
Additional contact information
Yunhe Zou: School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
Yaser Kiani: Faculty of Engineering, Shahrekord Univeristy, Shahrekord P.O. Box 115, Iran

Mathematics, 2023, vol. 11, issue 19, 1-18

Abstract: An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results in functionally graded media. To establish the governing equations of the plate, a quasi-3D plate model is used, which takes the non-uniform shear strains as well as normal strain through the thickness into account. With the aid of the Hamilton principle, the governing equations of the plate are established. For the case of a plate that is simply supported all around, natural frequencies are obtained using the well-known Navier solution method. The results of this study are compared with the available data in the open literature, and, after that, novel numerical results are provided to explore the effects of different parameters. It is depicted that, with the introduction of GPLs in the matrix of the composite media, the natural frequencies of the plate enhance. Also, a proper graded pattern in GPL-reinforced composite plates, i.e., an FG-X pattern, results in the maximum frequencies of the plate. In addition, the introduced quasi-3D plate theory is accurate in the estimation of the natural frequencies of thick nanocomposite plates at nanoscale.

Keywords: graphene platelet; nonlocal theory; quasi-3D plate model; Navier method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/19/4109/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/19/4109/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:19:p:4109-:d:1250172

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().