Nonlocal theory of elasticity in the natural vibrations of curved CNTs with defects

The current study presents the natural vibrations of single-walled carbon nanotubes (SWCNTs) using the nonlocal theory of elasticity. The study will help to develop nanodevices. The study focuses on the natural vibrations of curved or arch-like carbon nanotubes (CNTs). It is considered that the CNT has a crack-like defect and is simply supported (SS) at both ends. To model the equations of motion for the CNTs, a curved nanobeam approach is adopted, and the governing equations are solved using the separation of variables method. This research investigates the natural frequencies of three types of CNTs: armchair, zigzag, and chiral. A qualitative validation study demonstrates that the obtained results align with those published in the literature. Notably, the study reveals that small-scale effects and defects in the nanotubes influence the natural frequencies of CNTs.