Effects of residual stress and viscous and hysteretic dampings on the stability of a spinning micro-shaft

Abstract

This study examines the effects of the residual stress and viscous and hysteretic dampings on the vibrational behavior and stability of a spinning Timoshenko micro-shaft. A modified couple stress theory (MCST) is used to elucidate the size-dependency of the micro-shaft spinning stability, and the equations of motion are derived by employing Hamilton’s principle and a spatial beam for spinning micro-shafts. Moreover, a differential quadrature method (DQM) is presented, along with the exact solution for the forward and backward (FW-BW) complex frequencies and normal modes. The effects of the material length scale parameter (MLSP), the spinning speed, the viscous damping coefficient, the hysteretic damping, and the residual stress on the stability of the spinning micro-shafts are investigated. The results indicate that the MLSP, the internal dampings (viscous and hysteretic), and the residual stress have significant effects on the complex frequency and stability of the spinning micro-shafts. Therefore, it is crucial to take these factors into account while these systems are designed and analyzed. The results show that an increase in the MLSP leads to stiffening of the spinning micro-shaft, increases the FW-BW dimensionless complex frequencies of the system, and enhances the stability of the system. Additionally, a rise in the tensile residual stresses causes an increase in the FW-BW dimensionless complex frequencies and stability of the micro-shafts, while the opposite is true for the compressive residual stresses. The results of this research can be employed for designing spinning structures and controlling their vibrations, thus forestalling resonance.