Design and Experimental Demonstration of a Cyclically-Arranged Split-Ring Resonator Metamaterial With a Total Bandgap

Abstract We present a cyclically-arranged split-ring resonator metamaterial design that is capable of simultaneously attenuating P, SH, and SV-waves. The design targets tonal vibration frequencies in electric vehicles (EVs) caused by inverters and electric machines. The metamaterial’s plate-like nature facilitates straight-forward integration with unibody sheet metal structures commonly found in automotive applications. The basis for the unit cell is a sub-cell with nearly-coincident in-plane and out-of-plane resonant frequencies. This sub-cell effectively blocks SV-waves and P or SH-waves in a single polarization direction dependent on the resonator orientation. To achieve a total bandgap in all propagation directions, we cyclically rotate and replicate the sub-cell to form a unit cell containing 2×2 sub-cells. We then compute the unit cell’s band structure using a finite element model, documenting the expected bandgaps. To validate the numerical predictions, we fabricate a square polylactic acid plate embedded with 25 unit cells and subject it to P, SH, and SV-wave excitation on one edge using an electrodynamic shaker. We measure the displacement of the structure on the opposite edge using a laser Doppler vibrometer and compute the response transfer function. Results demonstrate significant attenuation of P, SH, SV-waves within the targeted frequency range of at least 35 dB, with SV-waves exhibiting the highest attenuation. This enhanced suppression of SV-waves is attributed to a greater number of sub-cells per unit cell participating in resonance compared to P and SH-waves. The measured performance demonstrates the strong potential for the proposed metamaterial to attenuate tonal frequencies in EV applications, potentially without additional mass.