The metasurface is widely used in wave manipulation because it has an excellent capability of phase modulation in a simple way. In this work, we propose an elastic metasurface that can achieve retroreflection of a flexural wave on a thin metal plate. The elastic metasurface is composed of only two subunits with a simplified design. By carefully selecting the thickness and material of the subunits, the phase of flexural wave is re-modulated, and retroreflection is achieved at different incident angles. Furthermore, a single-phase metasurface and a two-component metasurface with fixed constraints and free boundaries, respectively, are studied. The results show that this type of elastic metasurface conveniently steers reflection of the flexural wave, and it may have potential applications in vibration control, energy harvesting, and piezoelectric sensors.

The differential quadrature method has been developed to calculate the elastic band gaps from the Bragg reflection mechanism in periodic structures efficiently and accurately. However, there have been no reports that this method has been successfully used to calculate the band gaps of locally resonant structures. This is because, in the process of using this method to calculate the band gaps of locally resonant structures, the non-linear term of frequency exists in the matrix equation, which makes it impossible to solve the dispersion relationship by using the conventional matrix-partitioning method. Hence, an accurate and efficient numerical method is proposed to calculate the flexural band gap of a locally resonant beam, with the aim of improving the calculation accuracy and computational efficiency. The proposed method is based on the differential quadrature method, an unconventional matrix-partitioning method, and a variable substitution method. A convergence study and validation indicate that the method has a fast convergence rate and good accuracy. In addition, compared with the plane wave expansion method and the finite element method, the present method demonstrates high accuracy and computational efficiency. Moreover, the parametric analysis shows that the width of the 1st band gap can be widened by increasing the mass ratio or the stiffness ratio or decreasing the lattice constant. One can decrease the lower edge of the 1st band gap by increasing the mass ratio or decreasing the stiffness ratio. The band gap frequency range calculated by the Timoshenko beam theory is lower than that calculated by the Euler-Bernoulli beam theory. The research results in this paper may provide a reference for the vibration reduction of beams in mechanical or civil engineering fields.