Analyses of multi-bandgap property of a locally resonant plate composed of periodic resonant subsystems

A locally resonant (LR) plate made up of a thin plate attached with different types of resonators is analyzed in this paper. Each periodic element may consist of one or more spring-mass resonators attached onto one and the same surface of the plate lattice. The correctness of theoretical plane wave expansion (PWE) method adopted in this paper is validated through the comparisons with the classical theory and finite element method (FEM). When composing the LR plate system with two types of periodic resonant subsystems, there will appear two complete bandgaps, while other additional resonators may cause mainly directional gaps, calculated theoretically and numerically. From the comparisons of band-structure curves between a two-resonator-per-unit-element (TR-UE) system and both corresponding one-resonator-per-unit-element (OR-UE) systems, the bandgap width of the TR-UE system are not stacking effects of two OR-UE systems due to resonance interaction of different types of resonators. Moreover, via the deformation contours by FEM, the correspondence between the vibration modes of subsystems and the bandgap frequencies is demonstrated. The finite plate with limited resonators of two periodic types of parameters is modeled to show visually how flexural waves propagate within/without the bandgaps. Further, by adjusting the damping characteristic of both types of resonators, vibration attenuation band can be broadened widely.