Single input-single output coupled resonators with nonlinear self-excitation for multiple mass sensing

Abstract

A theoretical formulation and an experimental investigation into multiple mass sensing using self-excited coupled resonators is discussed. To construct a single input-single output (SISO) system, multiple resonators with different natural frequencies (frequency-mistuned resonators) are connected to a common shuttle mass, with resonators individually functionalized to absorb a specific analyte/mass. To measure the natural frequency shift of each resonator, we propose using the response frequency in the shuttle mass under the self-excitation, rather than the peak of the frequency response to the external harmonic excitation. Consequently, the method is applicable even in viscous environments where the frequency response curve does not exhibit a clear peak. The application of velocity feedback compensates for viscosity and selectively produces the self-excited oscillation, with one of the eigenfrequencies of the overall system corresponding to the natural frequency of the resonator absorbing the target analyte with the aid of band-pass filter. From the shift of the eigenfrequency corresponding to each resonator, changes in the masses absorbed to that resonator can be identified. A discrete mathematical model for the proposed sensing system is formulated and a nonlinear analysis was carried out to theoretically validate the control method. Furthermore, additional nonlinear feedback was introduced to prevent the infinite growth of the self-excited oscillation by ensuring that the sensing system behaves as a van der Pol oscillator. We experimentally investigated the efficiency of the method using a simple macro-scale apparatus with two resonators connected to a shuttle mass.