Band gaps and torsional vibration in a periodic shaft

Shafts used in torque and angular velocity transmission may behave as torsional vibration amplifiers due to resonance followed by unwanted vibrations. Many technologies are applied to attenuate vibration in certain frequency ranges in automotive, aerospace and industrial applications. More recently, using the concept of periodic structures (phononic crystals and metamaterials), it has been shown to be possible to obtain frequency band gaps where elastic waves cannot propagate and, therefore, standing waves cannot build up, thus avoiding resonance. Using a few periodic cells large attenuation can be obtained, so that the structure behaves like a mechanical filter. Investigations in periodic structure dynamics have been developed in recent years aiming at to attenuating specific and wide frequency ranges. The periodic structure can be a combination of different materials, or a unique material varying the geometry periodically. This work explores the possibility of using periodic shaft structures to create torsional band gaps for torsional vibration attenuation. Theoretical models and experimental results for torsional vibrations in a periodic shaft are investigated. The approach is to build a dynamic model using the Spectral Element Method (SEM), then calculating the dispersion diagram (wavenumber versus frequency) for the periodic cell and finally computing the forced response for a finite structure with a given number of cells and boundary and loading conditions. The geometry is designed to tune the bandgap range for a desired frequency range. The experimental dynamic response of a free-free shaft consisting of three cells excited at one end with and impact hammer and measured at the other end using an accelerometer is used to validate the SEM model. A good agreement is found. It is shown that modes that show up in the experimental response not predicted by the torsional SEM model can be explained by a torsional-bending coupling.