Free vibration analysis of couple stress rotating nanobeams with surface effect under in-plane axial magnetic field

This paper deals with the combination of surface and couple stress theories to examine free vibrational behavior of rotating functionally graded (FG) nanobeams under axial magnetic field. The theory introduces a scale parameter based on modified couple stress theory to capture the size effects. The modified couple stress theory is a weakly nonlocal theory and introduces the stiffness-hardening effect. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved by applying an analytical solution which satisfies clamped-free boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as length scale parameter, surface energy, angular velocity, magnetic field and power-law exponent on natural frequencies of rotary FG nanobeams in detail.