A subwavelength sinusoidally-shaped phononic beam structures-based metasurface for flexural wave steering

Abstract

In this work, we propose a method to design subwavelength metasurfaces for flexural waves in thin plates based on sinusoidally-shaped phononic beam structures. In the proposed method, the effective bending stiffness of sinusoidally-shaped phononic beam structures is tuned, and the effective phase velocity of the flexural waves is modulated subsequently by adjusting two key geometry parameters, namely, the amplitude of the sinusoidal profiles and lattice constants of the phononic beam structures. Compared with the previous methods, which modulate a single design parameter, the proposed method is a two-parameter modulating method. Thus, it not only maintains the functionality of metasurfaces, but also is much more flexible when obtaining a high wave transmittance. In addition, the mass of functional units of metasurfaces designed by the proposed method is not relevant to the design parameters, which is particularly important in weight-critical applications. To validate the feasibility of the proposed design method, the transmission spectra of sinusoidally-shaped phononic beam structures are modeled using the finite element method, and results are compared with experiments of 3D-printed samples. In addition, two representative metasurfaces, refractive and focusing metasurfaces, are designed with an available minimum transmission coefficient of 0.93 for functional units. Numerical evaluation of these metasurfaces’ performances confirms the effectiveness of the proposed method. This work paves a novel way to design elastic metasurfaces to manipulate flexural waves in thin plates and demonstrates a potential new direction to design metasurfaces for other wave types.