Effect of resonator location and boundary conditions on bandgap formation in a locally resonant beam metastructure

This study investigates how resonator placement and boundary conditions influence bandgap formation in a locally resonant beam metastructure. The steady-state response of the structure, subjected to a concentrated harmonic load, is then computed using the modal analysis. Four different boundary conditions are considered. For each boundary condition, the resonator array is shifted, and the corresponding responses are calculated. The study reveals that, for a cantilever beam, the widest bandgap occurs when the last resonator in the periodic array is positioned at the free end. For the other cases, no significant change in bandgaps is observed.