Poisson-like effect for flexural waves in periodically perforated thin plates

The Poisson-like effect, describing the redirection of waves by 90°, is shown to be feasible for flexural waves propagating in perforated thin plates. It is demonstrated that the lowest order symmetric leaky guided mode (S0 mode) is responsible for the splitting of wave motion in two orthogonal directions. The S0 mode shows a feature of stationary waves containing standing wave modes in one and two orthogonal directions for smaller and larger holes, respectively. The former case is well understood thanks to the phenomenon of Wood's anomaly, which was first observed in optical gratings supposed to be transparent. On the contrary, the strong scattering caused by the larger holes leads to a mixed mode occurring when the incident wave is totally transmitted. The mixed mode easily couples with the incoming waves and, therefore, the Poisson-like effect activated under this mechanism is much stronger. Using the Poisson-like effect, a device is proposed in which about 82% of the incident mechanical energy is redirected to the perpendicular direction. Results obtained with arrays of free holes also apply to inclusions with parameters properly chosen. The findings may provide applications in beam splitting and waveguiding.