A new periodic shaft model for broadband ultra-low-frequency vibration reduction in spinning shafts

Vibration isolation is found in periodic structures having a special feature known as vibration band gap. A periodic shaft model is proposed and analyzed in this study. This model is composed of a spinning solid shaft carrying periodic arrays of outer cantilever hollow shafts. The generalized differential quadrature rule (GDQR) method combined with the Bloch theorem is used to calculate the vibration band gaps of this periodic shaft. Results are verified by the forced vibration responses obtained using the GDQR method. Results indicate that for each length of the hollow shafts, there is a spinning velocity range for which the first band gap starts from zero frequency. In other words, each model of this periodic shaft can be used for vibration reduction over an ultra-low-frequency band gap at different spinning velocities. Results also indicate that there is a model with specific value of the hollow shafts length for which the second band gap is very close to the first band. For this model, the width of the ultra-low-frequency band gap is much greater than other models. Finally, verification of the GDQR method shows that it can be used as a precise numerical method for free and forced vibration analysis of the spinning shafts.