局域共振弹性超材料梁禁带宽度的拓宽方法

To address the issue of narrow band gap width in traditional local resonance clastic metamaterials, a design approach is introduced that employs non-uniformly distributed resonators to widen the band gap without modifying the total mass of the resonators. Firstly, a generalized elastic metamaterial beam model is established using the spectral element method (SEM), and the vibration transmission characteristics of both single-and double-layer metamaterial beams with uniform resonators arc analyzed. Subsequently, a design strategy for single-and double-layer metamaterial beams with non-uniform resonators is proposed while maintaining a constant total mass of the resonators. Finally, an experimental setup is devised to evaluate the vibration suppression performance of the proposed structures. The findings indicate that a wider band gap is achieved when there is a greater difference in eigenfrequencies between the resonators. However, the frequency response curve within the band gap range may exhibit significant fluctuations, which can be mitigated by introducing appropriate damping to stabilize the band gap curve. The band gap properties of the structure in double-layer metamaterial beams are influenced by both the mass ratio and damping of the resonators. Under the condition of equal mass between the resonators and the beam, the single-layer metamaterial beam with non-uniform and uniform resonators exhibits band gaps with widths of 440 Hz and 68 Hz, respectively. Similarly, the double-layer metamaterial beam with non-uniform and uniform resonators displays band gaps with widths of 395 Hz and 40 Hz, respectively. The study demonstrates that the proposed metamaterial structures effectively achieve vibration suppression, providing a novel approach to address vibration-related challenges in periodic structures.