Achieving transition between internal resonance and mode localization through coupling strength modulation

Abstract

Nonlinear mode coupling phenomena are prevalent in a wide range of dynamic systems, offering intriguing insights into the rich complexities of vibrational behavior. Internal resonance (IR) and mode localization (ML) are two typical mode coupling phenomena that have been widely studied and applied for sensing and energy harvesting. In this work, the transition between IR and ML has been studied theoretically and experimentally utilizing a mechanically coupled resonator, as well as its potential application has been explored. Numerical results of amplitude–frequency curves, phase–frequency curves, and the frequency veering curves under different internal and external conditions all indicate that the vibration behavior of the coupled resonator will transition from 1:1 IR region to ML region as the coupling stiffness increases. An equivalent experiment has also been implemented for verification, and its results are consistent with the theoretical and simulation ones. Furthermore, a self-powered sensor with a tunable coupling has been proposed, which can combine the advantage of IR for broadband energy harvesting and that of ML for ultra-high sensitivity mass detection.