Elastic Orbital Angular Momentum

We identify that flexural guided elastic waves in elastic pipes carry a well-defined orbital angular momentum associated with the compressional dilatational potential. This enables the transfer of elastic orbital angular momentum, that we numerically demonstrate, through the coupling of the compressional potential in a pipe to the acoustic pressure field in a surrounding fluid in contact with the pipe.

Figure 1

Schematic of an elastic spiral phase pipe (copper region) in a hollow elastic pipe (transparent region). Purely longitudinal waves, e.g., $L(0,2)$ modes (circular phase fronts), are mode converted into flexural $F(3,n)$ waves (helical phase fronts).

Figure 2

(a) Dispersion curves of guided waves in an aluminium pipe of inner diameter 40 mm and thickness 10 mm. Solid lines obtained by spectral collocation with points resulting from finite element computations. (b) Numerical evaluation (details reported in the Supplemental Material [25]) of the well-defined elastic OAM along the pipe axis, ${\mathcal{J}}_{Lz}$, associated with the dilatational potential for the lowest curves of the flexural modes $F(m,1)$.

Figure 3

Finite element time domain simulation of OAM transfer: (a) Schematic of the simulation domain, with pipe partially submerged 1 cm in water, surrounded by air. Arrows show axisymmetric longitudinal excitation position, with absorbing boundaries on exterior fluid walls. (b) Normalized compressional field in pipe [trace of the strain tensor, $\mathrm{tr}(ϵ)$] and pressure field ($P$) in the fluid at the end of the pipe ($z=0$). (c) Isosurfaces of fluid pressure in the region below the pipe showing spiraling acoustic waves, at the same time instance as in (b). Full details are shown in the Supplemental Material, along with frequency domain corroborations [25].