Flexural wave illusion on a curved plate

Abstract: Manipulating elastic waves using a transformation approach is challenging due to the complex constitutive relationship. However, for flexural waves, approximated as scalar waves, two straightforward approaches emerge based on geometric curvature and plate thickness. Here, we develop transformation theory to establish equivalence between curved plates of different shapes and thickness profiles. By introducing tailor-made thickness profiles on a given curved shape enables illusion effects, where flexural waves propagate as if on a flat plate or on another curved plate with totally different configuration. Numerical simulations and experimental field mapping confirm the effectiveness of these illusions. Our approach on flexural wave illusion finds applications in structural designs with material and shape constraints, and holds potential for vibration control, wavefront shaping, chaotic dynamics and topology control.