The propagation of flexural waves in a metamaterial plate with tunable low-frequency band gap

To efficiently attenuate flexural waves at low-frequency range (0–100 Hz) in the complex vibration environment, a metamaterial plate consists of steel, magnetorheological elastomer and cement-based piezoelectric composite (CPC) is proposed in this paper. The propagation of flexural waves in binary and ternary periodic material plate are studied by the plane wave expansion method (PWE) which combined with the Mindlin plate theory, and the frequency response functions are calculated by the finite element method (FEM). The dispersion curves under open and shorted electrical boundary conditions are considered, the regulation effect of bias magnetic field on the band gap is explored. The results show that material and geometric parameters significantly influence the band gap. Although the effect of electrical boundary conditions on the band gap can be ignored, the introduction of the CPC widens the width of band gap by 130%. The location and width of the band gap can be adjusted by varying magnetic field intensity, as magnetic field intensity \(H\) $H$ intensifies from \(0\text{ A}/\text{m}\) $0\text{A}/\text{m}$ to \(8\times {10}^{5} \text{A}/\text{m}\) $8\times {10}^5\text{A}/\text{m}$ , the band gap has a 25% increase. The proposed metamaterial plate has certain stiffness and strength, and it is suitable to be used in engineering. The results may provide an alternative avenue for understanding and optimizing the design of metamaterial plates with wide tunable band gaps.