Resonator positioning for enlarged bandgap in mechanical metastructure with finite resonators

Abstract

The positioning of resonators of locally resonant mechanical metastructure with finite resonators is presented to increase the bandgap. Based on the modal analysis solution of mechanical metastructure with finite resonators, the bandgap change according to aperiodic positioning of finite resonators under the fixed mass ratio of main structure to resonators is observed. By utilizing the responses of the main structure with single resonator having various positions, resonator positions for effective vibration attenuation are selected. Mountain frequencies overlapping between resonators is considered from the main structure responses with single resonator, positions for the enlarged bandgap width are obtained. By increasing the number of resonators and positions, mass distribution effect is added in bandgap formation according to resonators’ position of resonators. Using these results, effective resonator positions and mass distribution for each mode of mechanical metastructure with finite resonators under limited mass ratio of main structure to resonators are proposed.