Recommendation for the modelling of Donnell shell: The relationship between non-local parameter and frequency

Mohamed A. Khadimallah, Muzamal Hussain, Elimam Ali, Sehar Asghar and Abdelouhed Tounsi

Abstract

The vibration analysis of armchair, zigzag and chiral double-walled carbon nanotubes has been developed by inserting the nonlocal theory of elasticity into thin shell theory. First Donnell shell theory is employed while exercising wave propagation approach. Scale effects are realized by using different values of nonlocal parameters under certain boundary conditions. The natural frequencies have been investigated and displayed for various non-local parameters. It is noticed that on increasing nonlocal parameter, the frequency curve tends to decrease. The frequency estimates of clamped-free boundary condition are less than those of clamped-clamped and simply supported computations. The frequency comparisons are presented for armchair, zigzag and chiral nanotubes. The software MATLAB is used to extract the frequencies of double walled carbon nanotubes.

Key Words

boundary condition; Donnell shell theory; double-walled CNTs; nonlocal parameters; scale effect

Address

Mohamed A. Khadimallah and Elimam Ali: Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia Muzamal Hussain and Sehar Asghar: Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan Abdelouhed Tounsi: 1) YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea, 2) Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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