Forming Low-Frequency Complete Vibration Bandgaps in a thin Nonmetallic Elastic Metamaterial Plate

Low-frequency vibration-bandgaps in elastic metamaterials open new possibilities to minimize low-frequency vibration and noise. Unfortunately, fabricating a complete vibration bandgap for low frequencies still represents a challenging engineering task. In this paper, a new type of a low-frequency complete vibration bandgap in a thin non-metal elastic metamaterial plate is introduced and investigated numerically. The proposed elastic metamaterial plate consists of decoupling-resonators, which are deposited on a 2D, locally resonant phononic-crystal plate, made of an array of rubber fillers, which are embedded in a nonmetallic plate. The dispersion relationship, the power-transmission spectrum, and the displacement fields for the eigenmode are calculated using the finite element method. It is shown that coupling between the local resonance mode of the decoupling-resonators and the Lamb-wave mode of the epoxy plate, consistent with the modal superposition principle, is responsible for the formation of vibration bandgaps. Moreover, the equivalent spring-mass system for the coupling-resonators can be decoupled by introducing a rubber filler. In addition, both longitudinal and the transverse elastic wave bandgaps can be tuned to the same low-frequency range. As a result, a novel kind of low-frequency complete vibration bandgap, which can damp a low-frequency elastic wave, is produced. Furthermore, the effects of the decoupling-resonators on the vibration bandgap are investigated. It is now possible that an elastic metamaterial plate can be dampen with complete low-frequency vibration bandgaps, which can potentially be used for commercial noise and vibration reduction.