High efficiency generation of S-wave via a transmissive binary coding metasurface based on machine learning approach

Abstract

The well-known Lamb’s problem deals with the generation of surface and cylindrical body waves in an elastic half-space due to vertical point excitations on its surface. Owing to the potentials of S-waves in various engineering applications, the physical response of Lamb’s problem has inspired the authors to innovate a new idea for the generation of such S-waves by applying vertical excitations on an elastic half-space. An analytical model based on Lamb’s problem is established to study the elastic half-space wave motions under a vertical point load. Due to mathematical complexities in attaining the corresponding displacement fields, a machine learning approach is proposed to analyze the entire wavefield of the elastic half-space. Through a trained neural network, it is discovered that exertion of multiple vertical excitations with opposite magnitudes can induce beam splitting of transmitted S-waves. By optimizing the parameters, low R-waves and P-waves but high S-waves are observed in the wavefields predicted by the trained neural network. Analogous to excitations with opposite magnitudes, “0” and “1” coding elements that have out-of-phase response are introduced as a binary coding metasurface to investigate the feasibility of a binary coding metasurface in realizing beam splitting of transmitted S-waves via an input of P-waves. The beam splitting of transmitted S-waves is observed in both aluminum and elastomer thin plates. The outcome is significant and it proves that wave mode conversion of P-waves to S-waves is actualizable in both hard and soft materials through a transmissive binary coding metasurface, thus providing an avenue for various shear wave applications.