Multifunctional application of nonlinear metamaterial with two-dimensional bandgap

Mechanical metamaterials with low-frequency and broadband bandgaps have great potential for elastic wave control. Inspired by the ancient window mullions, a novel plate-type metamaterial with a two-dimensional bandgap is designed. Based on the local resonance mechanism, the broadband low-frequency in-plane and out-of-plane bandgaps on the designed structure are realized. The bandgaps can be adjusted by the mass re-distribution of the main-slave resonators, the stiffness design of the support beam, and the adjustment of the excitation amplitude. A semi-analytical method is proposed to calculate the in-plane and out-of-plane bandgaps and the corresponding wave attenuation characteristics of the infinite periodic metamaterial. We explored how mass re-distribution, stiffness changes, and geometric nonlinearity influence the bandgap. Then, to verify the conclusions, we fabricated a finite periodic structure and obtained its wave transmission characteristics both numerically and experimentally. Finally, the designed metamaterial is applied to the waveguide control, elastic wave imaging, and vibration isolation. This study may provide new ideas for structural design and engineering applications of mechanical metamaterials.