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Advances in Nano Research
  Volume 8, Number 4, May 2020 , pages 307-322

Theoretical impact of Kelvin\'s theory for vibration of double walled carbon nanotubes
Muzamal Hussain, Muhammad N. Naeem, Sehar Asghar and Abdelouahed Tounsi

    In this article, free vibration of double-walled carbon nanotubes (DWNT) based on nonlocal Kelvin\'s model have been investigated. For this purpose, a nonlocal Kelvin\'s model is established to observe the small scale effect. The wave propagation is employed to frame the governing equations as eigenvalue system. The influence of nonlocal parameter subjected to different end supports has been overtly examined. The new set of inner and outer tubes radii investigated in detail against aspect ratio. The influence of boundary conditions via nonlocal parameter is shown graphically. Due to small scale effect fundamental frequency ratio decreases as length to diameter ratio increases. Small scale effect becomes negligible on all end supports for the higher values of aspect ratio. With the smaller inner tube radius double-walled CNT behaves more sensitive towards nonlocal parameter. The results generated furnish the evidence regarding applicability of nonlocal model and also verified by earlier published literature.
Key Words
    free vibration; nonlocal material; double-walled CNTs; Kelvin\'s model; WPA
(1) Muzamal Hussain, Muhammad N. Naeem, Sehar Asghar:
Department of Mathematics, Government College University Faisalabad, 38000, Faisalabad, Pakistan;
(2) Abdelouahed Tounsi:
Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Algeria Faculty of Technology Civil Engineering Department, Algeria;
(3) Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

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