A Magnetic Tuning Mechanism to Compensate Frequency Ratio Deviation in Coupled Resonators for Improving Sensing Resolution With High Sensitivity

A magnetic tuning mechanism to compensate for the frequency ratio deviation in coupled resonators is proposed in this article for fulfilling the potential of nonlinear internal resonance (IR) to sensing applications. A magnetic tuning theory is constructed to deduce theoretical expressions of 1:3 IR with lumped parameter model and multiscale method. The effectiveness of the proposed magnetic tuning mechanism is experimentally demonstrated by taking a two-cantilever resonator system as an example, with 1:3 IR characteristics under different magnetic forces. The possibility to compensate for frequency ratio deviation caused by manufacturing, assembling, and other errors generated in production and service processes is further analytically and experimentally studied to improve sensing resolution and increase detection accuracy, achieving an adjustment range from 164.3 to 146.5 Hz in frequency and 1:2.83 to 1:3.17 in frequency ratio. The proposed compensation approach is believed to be universally applicable to cantilever-based sensors with the need for frequency matching.