Multi-frequency bandgap characteristics of multi-layer concentric ring-shaped locally resonant metamaterial plate

Abstract Low-frequency vibration control remains a core challenge in engineering. Addressing limitations of conventional locally resonant metamaterial plates in terms of narrow bandgap, inadequate low-frequency control capabilities, and complex structures that hinder mass production, this research proposes a multi-layer concentric ring-shaped locally resonant metamaterial plate (CRLRMP). This structure employs alternating concentric rings of elastic wrapper layers and rigid metal core columns to form multi-level resonant units. This design aims to excite and synergistically regulate multi-mode locally resonant coupling effects, thereby enabling effective manipulation of bandgap characteristics. This study integrates an improved plane wave expansion method (IPWEM) with the finite element method (FEM) to establish a computational analysis framework. It precisely reveals the dispersion energy band relationships, bandgap generation mechanisms, and elastic wave propagation patterns of CRLRMP structures under different configurations of concentric ring layers. Research findings indicate that as the number of concentric ring layers increases, the structure exhibits remarkable energy band splitting in its flexural and longitudinal vibration bandgaps. The number of bandgaps progressively increases, with the upper and lower frequency limits gradually extending toward higher and lower frequencies, respectively, while the total attenuation bandwidth remains relatively stable. Vibration transmission and time-domain analysis confirms that the propagation of elastic vibration waves within the bandgap frequency range is effectively suppressed, with vibrational energy confined within the resonant units. Parametric studies further elucidate the regulatory mechanisms of material and structural parameters on vibration transmission characteristics. The CRLRMP structure proposed in this study achieves controllable multi-frequency bandgap design while maintaining lightweight characteristics, providing an effective solution and new technical pathway for the application of plate-shell structures in low-frequency and broadband vibration control.