Abstract:A tunable transmitted three-tunnel helix unit cell is designed based on the working principle of the “screw-nut”. The length of the acoustic tunnel is changed by the screw-in depth of the screw, and then the phase of the transmitted waves can be tuned accordingly. The variations of the phase shift and transmittance of the unit cell with the screw-in depth and frequency are calculated by the finite element method. The generalized Snell's law of an flat surface is extended to an arc-shaped surface in this paper. The arch-shaped and toroidal metasurfaces are designed to regulate the wavefront of the transmitted acoustic wave. According to the presupposed acoustic function and the working frequency, the phase gradient of the metasurface and the screw-in depth of every unit can be determined by the generalized Snell's law of the arc-shaped surface and the variation of the phase shift of the unit cell with the screw-in depth. And the screw-in depth will be modified according to the variation of the transmittance of the unit cell in order to obtain the high transmission. The functional switch between the directional refraction, beam splitting and beam focusing for the arch-shaped metasurface is realized in a broadband frequency region. And the functional switch between the three-way splitting of wave beam, spiral wave generation and virtual movement of the source position is also realized for the toroidal metasurface. The full-field numerical simulations are performed by using the finite element method. And the experimental measurements are also carried out for both arch-shaped and toroidal metasurfaces. The experimental results have a good agreement with the numerical ones, which shows that the metasurfaces we designed are effective for the wavefront modulation of the transmitted acoustic waves. The study in this paper is relevant to the development of tunable irregular non-planar conformal acoustic devices.