The flexural-wave-based lens design for energy focusing via the trajectory prediction and the phase modulation

A plane lens that has the ability of focusing the flexural wave emitting from a point source into a focal point has been successfully designed by two methods, i.e., the trajectory prediction and the phase modulation. For the trajectory prediction, the lens makes the flexural waves along different paths arriving at the focal point simultaneously. For the phase modulation, the lens is designed via letting the waves producing the same phase at the theoretical focal position. Correspondingly, two media with the flexural wave velocity respectively larger and smaller than that in the matrix plate are adopted to construct the lens. The results show that the two methods are available because the wave energy at the actual focal positions has been respectively enlarged nearly 20 and 22 times after passing through the lens, compared with the case of a flat plate without any lenses. Meanwhile, both of lenses based on the two methods are broadband, and can work efficiently in the regions centered the designed frequency. Actually, not limited by the wave focusing phenomenon, the two methods presented in this paper are generalized applicable, which is exemplified by steering the flexural wave propagation at a random refraction angle.