  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.
