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Advances in Nano Research Volume 7, Number 6, November 2019 , pages 431-442 DOI: https://doi.org/10.12989/anr.2019.7.6.431 |
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Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity |
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Muzamal Hussain, Muhammad Nawaz Naeem, Abdelouahed Tounsi and Muhammad Taj
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| Abstract | ||
| Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. In current study, the Eringen\'s nonlocal elasticity theory with clamped-clamped and clamped-free end conditions is utilized for the vibration analysis of armchair and zigzag SWCNTs. The Fourier method is utilized to solve the ordinary differential equation. The motion equation for this system is developed using a novel wave propagation method. Complex exponential functions have been used and the axial model depends on BCs that has been described at the edges of CNTs. The behavior of different nonlocal parameters is considered to find the vibrational frequency of SWCNTs. It is exhibited that the effect of frequencies against aspect ratio by varying the bending rigidity. It has been investigated that by increasing the nonlocal parameter decreases the frequencies and on increasing the aspect ratio increases the frequencies for both the tubes. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid. | ||
| Key Words | ||
| nonlocal theory; WPA; carbon nanotubes; wave propagation approach; Fourier method | ||
| Address | ||
| (1) Muzamal Hussain, Muhammad Nawaz Naeem: Department of Mathematics, Govt. 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; (4) Muhammad Taj: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 1300, Azad Kashmir, Pakistan. | ||