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Structural Engineering and Mechanics Volume 88, Number 2, October25 2023 , pages 109-115 DOI: https://doi.org/10.12989/sem.2023.88.2.109 |
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Impact and post-impact of ring supports: Eigenfrequency response at nano-scale |
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Madiha Ghamkhar, Mohamed A. Khadimallah, Muzamal Hussain and Abdelouahed Tounsi
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| Abstract | ||
| In this paper, frequencies of zigzag structure of carbon nanotubes is investigated based on Donnell shell theory. These tubes are wrapped with the ring supports in the axial direction. The fundamental frequency curves displayed in article show the dependence of vibrations attributes to zigzag single walled carbon nanotubes. Various zigzag indices are introduced against the variation of length to predict the vibration. Also, the influence of ring supports is sketched with proposed structure for frequency analysis. The frequencies of zigzag tube decreases as the length increases. It is observed that the frequencies decreases with ring support and have higher frequencies without ring. The problem is formulated using Partial Differential Equation. Three expressions of modal deformation displacement functions is used for the elimination of temporal variation to form the solution in the eigen from. For the stability of present study the results are compared with experimentally and numerically in the open text. | ||
| Key Words | ||
| characteristic equation; eigen value; modal numbers; physical parameters | ||
| Address | ||
| Madiha Ghamkhar: Mathematics and Statistics Department, University of Agriculture, Faislabad, Pakistan Mohamed A. Khadimallah: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Muzamal Hussain: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan Abdelouahed Tounsi: YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia | ||