OICC Press Journal of Solid Mechanics 2008-7683 17 3 2025 11 24 Effect of mode number on radial vibration of single-walled carbon nanotubes with considering microstructural effect 321 338 10.60664/jsm.2025.1197346 EN Zahra Azimzadeh Department of Mathematics, College of Sciences, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran Alireza Fatahi-Vajari Department of Mechanical Engineering, Shahr.C., Islamic Azad University, Shahryar, Iran Journal Article 2025 11 24 In this paper, we studied the radial vibration of single-walled carbon nanotubes (SWCNTs) using doublet mechanics (DM) with a scale parameter in different mode numbers. To this end, first we derived the partial differential equation that governs the radial vibration of SWCNTs. It is the first time that the radial vibration of SWCNTs is obtained simultaneously with respect to mode number and scale effect. To obtain the natural frequency and dynamic response of the radial vibration, the equation of motion is solved and the relation between natural frequency and mode number along with scale parameter is derived. Unlike the other methods, this analytical formula is explicitly dependent to mode number and chirality effect. The effects of varying some geometrical and mechanical parameters of SWCNT on radial frequency have been investigated, too. It is shown that the mode number and scale parameter have important effects in the radial vibration response of SWCNTs. The mode number along with scale parameter decreases the radial frequency in comparison with the estimations of the classical models. However, as the tube diameter increases, reduction of this effect on the natural frequency happens. This effect is more apparent in lower tube diameter. It is also shown that in the same condition, the Armchair nanotube has higher frequency than the Zigzag one. To validate the accuracy and ability of this method, the obtained results herein using DM are compared with the existing results of the other methods such as theoretical and experimental and good agreement is seen.