Thermal vibration of armchair, chiral, and zigzag types of single walled carbon nanotubes using a nonlocal elasticity theory: An analytical approach

Abstract This research delves into the study of thermal vibration characteristics exhibited by three distinct types of Single‐Walled Carbon Nanotubes (SWCNTs): armchair, chiral, and zigzag configurations. The investigation is carried out using Navier's technique, which integrates a non‐local elasticity theory and Euler‐Bernoulli beam theory, providing a comprehensive understanding of carbon nanotubes (CNT) behavior under varying temperature conditions. To explore these characteristics, governing equations for vibrations are derived based on Hamilton's principle, incorporating both non‐local stress resultants. These equations are instrumental in computing the natural frequencies of Hinged‐Hinged (HH) SWCNTs subjected to low (room) and high‐temperature conditions. A detailed exploration is conducted to evaluate the influence of several key scaling parameters. These parameters encompass small‐scale effects, temperature variations, the thermal environment, and the length‑to‑thickness ratio of the CNTs, scrutinizing their impact on the first and second mode natural frequencies. This comprehensive assessment sheds light on the multifaceted interplay between these factors and the resulting vibration behaviors in SWCNTs.