Numerical and Experimental Investigations on Tunable Low-frequency Locally Resonant Metamaterials

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In this paper, a tunable locally resonant metamaterial is proposed for low-frequency band gaps. The local resonator composed of two pairs of folded slender beams and a proof mass is designed based on the theory of compliant mechanism. The design optimization on geometric parameters is carried out to fulfil the quasi-zero-stiffness property. The locally resonant metamaterial is formed by periodically arranged unit cells, and the transmittance of longitudinal wave is studied through three aspects: numerical predictions, finite element simulations and experimental tests. The variation trends revealed by these three methods match well with one another: the band gap moves to lower frequency and both its depth and width get smaller and smaller with the increase of pre-compression (\(\Delta \)). The band gap overlays the frequency range of 73.10–92.38 Hz and 16.78–19.49 Hz at \(\Delta = 0 \, \hbox {mm}\) and \(\Delta = 10 \, \hbox {mm}\), respectively, providing a wide range of tunability. Besides, the ultralow-frequency band gap can be achieved as \(\Delta \) approaches 10 mm. This study may provide an avenue for achieving the tunable ultralow-frequency locally resonant band gap.

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The authors gratefully acknowledge the support from the National Natural Science Foundation of China (11972152, 11832009), the National Key R&D Program of China (2017YFB1102801), and the Laboratory of Science and Technology on Integrated Logistics Support.

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Correspondence to Jiaxi Zhou.

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Lin, Q., Zhou, J., Pan, H. et al. Numerical and Experimental Investigations on Tunable Low-frequency Locally Resonant Metamaterials. Acta Mech. Solida Sin. (2021).

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  • Acoustic metamaterial
  • Locally resonant band gap
  • Tunability and ultralow frequency
  • Quasi-zero stiffness