Longitudinal-flexural wave mode conversion via periodically undulated waveguides with constant and graded profiles

Wave mode conversion allows to transform energy from one propagating wave type to another at a boundary where a change in material properties or geometry occurs. Converting longitudinal waves to flexural ones is of particular interest in elasticity due to their significant displacement amplitudes, facilitating detection at the surface for practical applications. Typically, the design of wave conversion devices requires (i) the use of locally resonant structures with a spacing much shorter than the associated wavelengths, or (ii) architected media whose effective properties yield efficient mode conversion at selected frequencies. In both cases, the realization of these devices may incur in fabrication difficulties, thus requiring alternative solutions based on simpler designs that can retain the wave manipulation capabilities of interest. In this paper, we propose the use of single-phase periodically undulated beams to design phononic crystals that achieve wave mode conversion between longitudinal and flexural waves. We derive the corresponding dispersion relations using the plane wave expansion method and demonstrate that the coupling between longitudinal and flexural wave modes can be manipulated using an undulated profile, generating mode veering with inverted group velocities. The wave conversion mechanism is verified both computationally and experimentally, showing good agreement. Our findings indicate a versatile design strategy for phononic crystals with efficient wave conversion property, enabling applications in structural health monitoring, sensing, and non-destructive testing.