Higher-order defective metamaterial for multi-band low-frequency vibration localization

Defective metamaterials offer significant potential for applications in filtering, sensing, waveguiding, and energy harvesting, owing to defect states capable of localizing vibrational energy. However, constraints from Bragg scattering typically restrict these states to high-frequency ranges, and they are sparse within a single bandgap. Conventional strategies that add multiple defects broaden the spectrum but suffer from inter-defect dispersion that weakens energy concentration. In this study, a novel defective rhombic metamaterial (DRM) is proposed to achieve multi-band low-frequency defect states from a single-point defect. The novelty rests on two mechanisms: (1) the rhombic geometry’s low effective stiffness significantly lowers the bandgap frequency without enlarging lattice size; and (2) the DRM supports higher-order defect states, enabling multiple localized modes to coexist within a single bandgap while maintaining strong localization. The band structures of the DRM are first analysed using finite element (FE) simulations, demonstrating the concept of low-frequency higher-order defect modes. Subsequently, the spectral element method (SEM) is employed to evaluate the transmittance characteristics, followed by parametric studies to explore the influence of geometric parameters on energy-localization behavior. Finally, the theoretical and numerical predictions are validated experimentally, providing the first experimental evidence of higher-order defect modes in the sub-kilohertz range. Overall, this work presents a promising strategy for broadband low-frequency energy localization using compact single-point-defect metamaterials, paving the way for higher power density in miniaturized energy harvesters and enhanced resolution in sensing applications.