Vibration Analysis of Single-Walled Carbon Nanotubes Embedded in a Polymer Matrix under Magnetic Field Considering the Surface Effect Based on Nonlocal Strain Gradient Elasticity Theory

Single-walled carbon nanotubes (SWCNTs) in an elastic medium under a longitudinal magnetic field have piqued the interest of researchers as elements utilized in nanoelectro-magneto-mechanical systems (NEMMS). This work presents the vibration analysis of embedded SWCNTs using the nonlocal second-order strain gradient elasticity theory. Considering the surface effect, the characteristic equation of motion for a SWCNT embedded in a polymer matrix under a longitudinal magnetic field is formulated and derived. The dependence of the distinct natural frequency of SWCNTs on the nanotube chiral angle and diameter is clarified. The effects of various parameters on the vibration characteristics of SWCNTs are examined and discussed, including the longitudinal magnetic field, surface effect, chiral index, chiral angle, chirality of SWCNTs, vibrational mode number, aspect ratio (length-to-diameter ratio), nonlocal and material length scale parameters. The numerical findings of this work might be helpful in the study and implementation of embedded SWCNTs as NEMMS devices.