Manipulation of the first stop band in periodically corrugated elastic layers via different profiles

Abstract We demonstrate the manipulation of the first frequency bands by changing the periodic corrugations on the surfaces of elastic plates. Based on the Fourier analysis and Floquet theorem, we have derived the dispersion relations for elastic waves propagating in periodically corrugated plates with different geometric profiles, which can always lead to the creation of forbidden bands. The effects of corrugation profiles on the forbidden bands have been quantified by the introduced shape factor, which has been proved to be proportional to the bandwidth. The simulations have confirmed the effects of surface geometries on the bandwidth, which is linearly dependent on the shape factor and corrugation amplitude. The calculated shape factor from the simulated data is very close to its theoretical value, verifying the applicability of the proposed band manipulation mechanism. The theoretical and numerical results indicate that the desired forbidden band could be obtained by selecting the corrugation geometries with the optimal shape factor and corrugation amplitude, which provides an efficient way to realize elastic wave filters and band gap materials in vibration control engineering.