Reciprocal dynamics in nonlinear systems

Abstract

Nonreciprocal vibration transmission is an important problem from a fundamental perspective and because of the additional functionalities that it enables in mechanical or acoustic devices. A common realization of nonreciprocal dynamics relies on implementation of nonlinear internal forces within the system. In this talk, we identify and discuss different manifestations of nonreciprocity in nonlinear systems. As a necessary condition, nonreciprocal dynamics is realized in nonlinear systems with broken mirror symmetry. We show that a second symmetry-breaking parameter can counteract the original asymmetry and ultimately restore reciprocal dynamics in a system with broken mirror symmetry, even near the system resonances. Thus, breaking the mirror symmetry is a necessary but insufficient condition for realizing nonreciprocity in nonlinear systems. We also highlight the contribution of phase to nonreciprocal vibration transmission by discussing response regimes that are characterized by nonreciprocal phase shifts. Our findings showcase the potential of asymmetry to serve as an additional design parameter for devices that operate based on nonreciprocity.