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Advances in Nano Research
  Volume 8, Number 3, April 2020 , pages 229-244

Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis
Muzamal Hussain, Muhammad N. Naeem and Abdelouahed Tounsi

    In this paper, modified Kelvin's model has been used to analyze the orthotropic vibration frequencies of single walled carbon nanotubes with clamped-clamped and clamped-free boundary conditions. For this system the governing equation is developed with wave propagation approach. Armchair, zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different modes, in-plane rigidity and mass density per unit lateral area. Throughout the computations, on decreasing the length-to-diameter ratios, the frequencies of said structure increases. In addition, by increasing three different value of in-plane rigidity resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. The results generated using computer software MATLAB to furnish the evidence regarding applicability of present model and also verified by available published literature.
Key Words
    CNTs; wave propagation approach; Kelvin Model; bending rigidity
(1) Muzamal Hussain, Muhammad N. Naeem:
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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