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

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.