Size-dependent vibrations of axially moving carbon nanobeam located in the magnetic field

The size-dependent free vibrations of nanobeams with axial motion in thermo-magnetic environments are examined using the non-local Rayleigh theory. The vibration equations have been derived using Hamilton's principle. The Galerkin technique has been utilized to determine the backward and forward vibration frequencies as well as the instability thresholds of the system. Comparative studies have been conducted to validate the results of this study. Some key parameters have been evaluated about the vibrations of the nanobeam, such as the magnetic field intensity, the speed of the axial movement, and the ratio of bending stiffness. The results showed that magnetic fields improved the performance of the system. Additionally, it was demonstrated that increasing the rotational inertia parameter reduces vibration frequencies and system stability.