Invisible omnidirectional lens for flexural waves in thin elastic plates

A feasible approach is proposed in this work to realize an acoustic omnidirectional invisible lens for flexural waves in thin elastic plates. These devices require extreme values of the refractive index close to its center, and in this work this drawback is overcome by reducing gradually the thickness of the elastic plate, which has the same effect as increasing proportionally the refractive index. Although ideally the thickness of the plate should be zero at the central point, it is shown that a finite but small minimum thickness is enough to provide a good invisibility effect. Numerical simulations are performed by the finite element method, which supports the theoretical predictions, showing that an invisible lens is feasible for flexural waves.