Flexural wave illusion on a curved plate

TL;DR

This paper develops a transformation theory for flexural waves on curved plates, enabling wave illusions by tailoring thickness profiles, with confirmed simulations and experiments, advancing wave manipulation in structural design.

Contribution

It introduces a novel transformation approach for flexural waves on curved plates, allowing wave illusions through tailored thickness profiles, which was not previously achievable.

Findings

Numerical simulations confirm wave illusion effects.

Experimental mapping validates the theoretical approach.

The method enables control of wave propagation on complex structures.

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.