Energy Transfer into Period-Tripled States in Coupled Electromechanical Modes at Internal Resonance

TL;DR

This paper demonstrates controllable energy transfer into period-tripled states in coupled electromechanical modes at internal resonance, revealing multistability and potential applications in mechanical memory and complex system modeling.

Contribution

It introduces a method to achieve and control period-tripled states in coupled resonators, expanding understanding of energy transfer and multistability in nonlinear vibrational systems.

Findings

Energy transfer to period-tripled states is controllable.

Multiple coexisting phase states are observed in the lower mode.

Potential applications in ternary logic and complex system simulation.

Abstract

Efficient energy transfer often occurs between oscillation modes in a resonator when they are tuned to internal resonance. We design the eigenfrequencies of two vibrational modes of an electromechanical resonator to be close to a ratio of 3:1 and demonstrate that the energy supplied to the upper mode can be controllably transferred to the lower mode. With the lower mode vibrating with a period tripled that of the upper mode, the discrete time-translation symmetry imposed by the periodic drive is broken. The lower mode settles into one of three stable period-tripled states with different phases. This channel for energy transfer from the upper mode can be turned on or off without changing system parameters. When the upper mode itself becomes multistable under strong resonant or parametric drive, additional sets of coexisting period-tripled states emerge in the lower mode. In the latter case, we measure a total of 6 coexisting vibration states with identical amplitude but phases differing by $\pi$/3. Excitation of coexisting states with three different phases could open new opportunities in designing mechanical memory based on ternary logic. Coupled resonators with period-tripled states can also be used to model complex interacting systems with spin equals one.