Mechanical circulator for elastic waves by using the nonreciprocity of flexible rotating rings

- Nonreciprocal effect is demonstrated for the first time in flexible rotating rings.
- Rotation and damping create double asymmetry in the dispersion diagrams of rings.
- Optimal frequencies for isolation/transmission are derived analytically.
- A mechanical circulator composed of rotating ring and attached beams is investigated.
- A spectral matrix for rotating rings in an Eulerian reference frame is derived.

Circulators have a wide range of applications in wave manipulation. They provide a nonreciprocal response by breaking the time-reversal symmetry. In the mechanical field, nonlinear isolators and ferromagnetic circulators can be used for this objective. However, they require high power and high volumes. Herein, a flexible rotating ring is used to break the time-reversal symmetry as a result of the combined effect of Coriolis acceleration and material damping. Complete asymmetry of oscillating and evanescent components of wavenumbers is achieved. The elastic ring produces a nonreciprocal response that is used to design a three port mechanical circulator. The rotational speed for maximum transmission in one port and isolation in the other one is determined using analytical equations. A spectral element formulation is used to compute the complex dispersion diagrams and the forced response. Waveguides that support longitudinal and flexural waves are investigated. In this case, the ring nonreciprocity is modulated by the waveguide reciprocal response and the transmission coefficients can be affected. The proposed device is compact, nonferromagnetic, and may open new directions for elastic wave manipulation.