Search for: All records

Abstract This article studies the nonreciprocity of a system that consists of a bistable element coupled to a monostable element through a contactless magnetic interaction. To illustrate the concept, the bistable element is physically realized using a pendulum that interacts with a stationary magnet and the monostable element is a classical pendulum. A numerical model is implemented to simulate the nonlinear dynamics of the system. Both simulations and experiments show that the system exhibits a strong amplitude-dependent nonreciprocity in response to initial excitations. At small input amplitudes, the system has an intrawell response with minimal transmission of energy whether the excitation is exerted on the side of the bistable pendulum or on the other side. However, at high input amplitude, a strong nonreciprocal behavior is observed: excitation of the bistable pendulum causes an interwell response which considerably reduces the distance between the two pendulums and allows energy to be efficiently transmitted through the contactless magnetic interaction; excitation of the monostable pendulum does not cause any interwell response and results in limited energy transmission. The combination of bistability and contactless nonlinear interactions allows the system to exhibit very strong amplitude-dependent nonreciprocity, which may be useful in a wide range of applications. 

Parity-time (PT) symmetry was first studied in quantum mechanical systems with a non-Hermitian Hamiltonian whose observables are real-valued. Most existing designs of PT symmetric systems in electronics, optics, and acoustics rely on an exact balance of loss and gain in the media to achieve PT symmetry. However, the dispersive behavior of most loss and gain materials restricts the frequency range where the system is PT symmetric. This makes it challenging to access the exceptional points of the system to observe the PT symmetric transition dynamics. Here, we propose a new path to realize PT symmetric systems based on gyroscopic effects instead of using loss and gain units. We demonstrate that PT symmetry and the occurrence of exceptional points are preserved for inversive, counter-rotating gyroscopic systems even with dispersive sub-units. In a gyroscopic system with two circular rings rotating in opposite directions at the same speed, the spontaneous symmetry breaking across the exceptional points results in a phase transition from a moving maximum deformation location to a motionless maximum point. The motionless maximum point occurs despite the externally imposed rotation of the two rings. The results set the foundation to study nonlinear dispersive physics in PT symmetric systems, including solitary waves and inelastic wave scattering.