Magneto-hygro-thermo-mechanical vibration analysis of spinning nanobeams with axisymmetric cross-sections incorporating surface, rotary inertia, and thickness effects

This work analyzes the scale-dependent dynamics and stability of spinning beams with circular and rectangular cross-sections in complex environments based on the nonlocal strain gradient theory (NSGT). To model the system, surface energy, rotary inertia effect, and scale effects along the thickness direction are considered. The surface elasticity theory and Rayleigh beam model are adopted to extract the dynamical equations. The eigenvalue problem is solved by employing the Laplace transform and the Galerkin discretization procedure, and the vibrational frequencies are detected accordingly. Also, according to the stability theory of gyroscopic systems, the system instability threshold is recognized analytically. Campbell diagrams and stability graphs are examined for comprehending the divergence and flutter behaviors. The impacts of geometry, scale factor, asymmetrical cross-sections, thermal fields, hygro-magnetic loads, follower and axial forces, and various shear and elastic foundations on the dynamical behavior of the system are interpreted. The results revealed that the system stability evolution could be substantially altered by considering the rotary inertia effect and variations of the crosssection geometry. It is demonstrated that, unlike the rotary inertia effect, the stable regions of the system are significantly expanded by considering the scale effects along the thickness direction. It is also found that the stabilizing effect of surface energy is amplified for low/high values of the diameter/length. The present research outcomes can offer valuable practical guidelines for spinning nanoengineering applications.