Design of multi-bandgap metamaterial plate based on composite cylindrical resonators - Zhi Miao; Jianfei Yin; Yu Yang; Yibo Ke; Zhoufu Zheng; Xiaoming Geng; Qian Wang (Materials & Design)
This paper introduces a composite locally resonant metamaterial plate (CLRMP) designed for broadband, low-frequency vibration suppression through multi-resonance and gradient configurations. Theoretical models employing the plane wave expansion method are developed to compute the band structures of the CLRMP. For rapid evaluation of the bandgap bounding frequencies, closed-form formulas are derived using wave theory in conjunction with Hamilton's principle. The composite arrangement of local resonators achieves two low-frequency bandgaps, effectively expanding the bandgap region and enhancing the designability of bandgaps compared to traditional locally resonant plate. Building on the initial composite model, two methods are employed to further broaden the bandgaps. The first method utilizes a genetic algorithm to optimize the bandgap width of the CLRMP with periodically arranged resonators. Additionally, a nonperiodic gradient design is proposed by adjusting the stiffness of the resonators to ensure that the natural frequencies of the nonperiodic resonators are lower than those of the periodic resonators. This design approach demonstrates a significant 67.9% increase in normalized attenuation bandwidth. Experimental results reveal an average vibration suppression of 21.4 dB in the 250 Hz to 650 Hz range for the nonperiodic metamaterial plate, outperforming periodic designs in low-frequency vibration absorption and achieving broader attenuation bands.