Free vibration analysis of nanoscale spinning shafts based on Eringen's differential constitutive elastic model by using generalized differential quadrature method

Abstract

The free vibration behavior of spinning nanoshafts is critically examined through the framework of nonlocal elasticity. Combining the Euler-Bernoulli beam model with the Eringen's nonlocal theory, this work formulates a scale-dependent mathematical model. Hamilton's principle is employed to derive the nonlocal governing equations and associated boundary conditions. The generalized differential quadrature method (GDQM) is utilized to discretize and solve the resulting eigenvalue problem. Numerical results systematically quantify  how the small-scale parameter, angular velocity, and various boundary conditions affect the system's fundamental and second mode forward and backward frequencies. Additionally, the impact of geometrical properties, such as the aspect ratio and thickness-to-diameter ratio, on the instability thresholds is investigated. The findings of this study offer valuable guidelines for enhancing the performance and stability of advanced rotating nano-electromechanical systems (NEMS).