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Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)-Substrate Medium Systems

Limkatanyu, Suchart; Sae-Long, Worathep; Sedighi, Hamid M.; Rungamornrat, Jaroon; Sukontasukkul, Piti; Imjai, Thanongsak; Zhang, Hexin


Suchart Limkatanyu

Worathep Sae-Long

Hamid M. Sedighi

Jaroon Rungamornrat

Piti Sukontasukkul

Thanongsak Imjai


This paper proposes a novel nanobar-substrate medium model for static and free vibration analyses of single-walled carbon nanotube (SWCNT) systems embedded in the elastic substrate medium. The modified strain-gradient elasticity theory is utilized to account for the material small-scale effect while the Gurtin-Murdoch surface theory is employed to represent the sur-face-energy effect. The Winkler-foundation model is assigned to consider interactive mechanism between the nanobar and its surrounding substrate medium. Hamilton’s principle is called for to consistently derive the system governing equation, initial conditions, and classical as well as non-classical boundary conditions. Two numerical simulations are employed to demonstrate the essence of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on static and free vibration responses of single-walled carbon nanotube (SWCNT)-substrate medium systems. The simulation results show that the material small-scale effect, the surface-energy effect, and the interaction between the substrate and the structure lead to a system-stiffness enhancement both in static and free vibration analyses.

Journal Article Type Article
Acceptance Date May 17, 2022
Online Publication Date May 19, 2022
Publication Date 2022
Deposit Date May 17, 2022
Publicly Available Date May 19, 2022
Journal Nanomaterials
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 12
Issue 10
Article Number 1740
Keywords Free vibration; nanobar; modified strain-gradient theory; surface-elasticity theory; elastic substrate media; Hamilton’s principle
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