The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling

Abstract

The powerful non-classical continuum theory of strain gradient elasticity is capable of effectively capturing small-scale effects in micro-structures. Based on this theory, a formulation is developed to investigate the coupled torsional-flexural vibrations of micro-rotors in the presence of inertia nonlinearities arising from the eccentricity and gyroscopic motion of the rotors. With the aid of a weighted-residual technique, coupled nonlinear partial differential equations of motion are truncated into a discrete model. Then, the resonance of the fundamental mode of the torsional vibration excited by the flexural vibration is investigated by utilizing the perturbation method of multiple scales. Moreover, a numerical simulation approach is conducted to confirm the validity of the analytical solution proposed by the multiple scales perturbation method. Obtained results for the resonant frequency and amplitude of the fundamental torsional mode indicate that the strain gradient theory can predict far more reliable results than the classical continuum mechanics for micro-rotors with very thin shafts.