Deflecting incident flexural waves by nonresonant single-phase meta-slab with subunits of graded thicknesses

We propose a nonresonant single-phase meta-slab with subunits of graded thicknesses for deflecting incident flexural waves. Analytic solutions of the transmission coefficient and the phase shift for the subunits are derived by the transfer matrix method (TMM). A theoretical formula related to the path length of the travelling wave is given to predict the phase shift. Finite element (FE) simulations for wave propagations in the subunits are conducted, and they verify the analytic solutions and the theoretical prediction. Based on these theoretical and numerical work, we design the meta-slab to deflect incident flexural waves according to the generalized Snell's law (GSL). Corresponding FE simulations and experiments are performed. Good agreements between them are observed. They evidence that the designed meta-slab can deflect incident flexural waves in a broad frequency range. Our study presents a method of designing meta-structures with simple configurations for controlling flexural waves, which is conductive to vibration isolation, acoustic radiation reduction, and energy harvesting.