Split Ring Resonator-based Metamaterial with Total Bandgap for Reducing NVH in Electric Vehicles

We propose a novel Split Ring Resonator (SRR) metamaterial capable of achieving a total (or complete) bandgap in the material’s band structure, thereby reflecting airborne and structure-borne noise in a targeted frequency range. Electric Vehicles (EVs) experience tonal excitation arising from switching frequencies associated with motors and inverters, which can significantly affect occupant perception of vehicle quality. Recently proposed metamaterial designs reflect airborne noise and structure-borne transverse waves over a band of frequencies, but do not address structure-borne longitudinal waves in the same band. To achieve isolation of acoustic, transverse, and longitudinal elastic waves associated with tonal frequencies, we propose a metamaterial super cell with transverse and longitudinal resonant frequencies falling in a total bandgap. We calculate the resonant frequencies and corresponding mode shapes using finite element (FE) modal analysis. We obtain the unit cell band structure by applying Floquet-Bloch boundary conditions to a single cell and subsequently solve the associated eigenvalue problem. We compute the out-of-plane polarization of the eigenmodes to further distinguish between in-plane and flexural bandgaps. The resonant frequencies depend on the material used and the physical dimensions of the unit cell features. Using aluminum, we design the super cell to exhibit resonant frequencies and a total bandgap near 10 kHz, which is typically observed in the frequency content of inverter noise. Scaling the unit cell size also offers a predictable shift in the resonant frequencies, and thereby bandgap, offering adaptability for regulating various frequency emissions under consideration. Further, we assess the frequency response functions of the structure-borne vibration transmission using FE analysis and evaluate the sound transmission loss (STL) of the metamaterial using simulations accounting for coupled acoustic-structure interactions. Our proposed metamaterial is based on plate-like and shell-like structures commonly employed in automotive design, and thus can serve as a cost-effective and lightweight alternative to traditional sound-deadening materials.