Passive Nonreciprocity in a System of Asymmetrical Rotational Oscillators

In this paper we investigate an elastically linked, nonlinear, in-plane rotator system and experimentally study its nonreciprocal impulse response. The nonlinearity of the system arises from the angled elastic linkage in rotational motion. A chain of rotators coupled with such linkages reaches an acoustic vacuum when the pretension of the elastic links vanish, leading to large nonlinearity tunable via small pretension. Using an analytical model and experimental exploration, we observe a broadband nonreciprocity in a weakly pretensioned, asymmetric, three-rotator system. In addition, we use a nonlinear normal-mode (NNM) analysis, capturing the main qualitative dynamics of the response, to explain the observed nonreciprocity mechanism. The analysis shows that equal applied impulses, combined with energy-dependent frequency and mode shapes, result in robust nonreciprocity features, contrary to the reciprocal response present in the linear counterpart of this system.