Real-space topological singularities in structured flexural waves

Real-space singularities underpin diverse wave phenomena yet remain largely unexplored in elastic wave systems. We report the observation of real-space topological singularities in structured flexural waves on finite-sized solids. These singularities are robust against perturbations and annihilate only through topological phase transitions. Moreover, they imprint dislocation lines on the radiated sound field, generating acoustic vortices in free space from an achiral source and structure. Our findings bridge continuum mechanics and topological physics, establishing elastic waves as a platform for exploring complex topological textures in real space and paving the way towards singular phononics.