Band gap generation in cantilever beams through periodic material removal

Abstract

Traditional methods for generating band gaps in beams usually involve adding periodic elements like tuned mass dampers or masses, or applying complex geometrical changes. This research suggests a subtraction-based method achieved by removing material in the thickness direction through straightforward machining operations, thus forming periodic cells. The numerical studies start with band gap analysis, using periodic theory to assess different periodic cell configurations. This is followed by numerical and experimental studies on cantilever beams, each containing a set number of these periodic cells. Non-contact vibration measurements are conducted on one plain and six machined aluminum beams using a multipoint laser vibrometer and an automated impact hammer. The experimental findings corroborate the band gaps predicted by the numerical model, confirming the effectiveness of this approach. The study notes that the optimal periodicity of the cells and the contrast in thickness vary with the beam’s dimensions, and that the thickness contrast markedly affects the quantity, width, and intensity of the resulting band gaps. These results indicate that (1) periodic material removal in beam-like structures allows improved vibration reduction while mass is reduced, and (2) manufacturing can play a key role in vibration control in simple structures.