Correlation between frequency and Poisson's ratio: Study of durability of armchair SWCNTs

Muzamal Hussain , Mohamed A. Khadimallah , Abdelouahed Tounsi

Abstract

An analysis of the Poisson's ratios influence of single walled carbon nanotubes (SWCNTs) based on Sander's shell theory is carried out. The effect of Poisson's ratio, boundary conditions and different armchairs SWCNTs is discussed and studied. The Galerkin's method is applied to get the eigen values in matrix form. The obtained results shows that, the decrease in ratios of Poisson, the frequency increases. Poisson's ratio directly measures the deformation in the material. A high Poisson's ratio denotes that the material exhibits large elastic deformation. Due to these deformation frequencies of carbon nanotubes increases. The frequency value increases with the increase of indices of single walled carbon nanotubes. The prescribe boundary conditions used are simply supported and clamped simply supported. The Timoshenko beam model is used to compare the results. The present method should serve as bench mark results for agreeing the results of other models, with slightly different value of the natural frequencies.

Key Words

clamped simply supported; natural frequencies; Poisson's ratio; Sander's shell theory

Address

Muzamal Hussain — Department of Mathematics, Govt. College University Faisalabad, 38000, Faisalabad, Pakistan
Mohamed A. Khadimallah — 1) Department of Civil Engineering, College of Engineering in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia, 2) Laboratory of Applied Mechanics and Engineering LR-MAI, University Tunis El Manar- -ENIT BP37- Le belvédère, 1002, Tunisia
Abdelouahed 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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