On a principle for mass sensing using self-excited template dynamics of coupled oscillators and root-finding algorithms

In this work, we analyze a mass sensing mechanism that relies on self-excited template dynamics of a simple network of two coupled oscillators, one linear and one nonlinear, to detect changes in the mass of the linear oscillator with tunable sensitivity. The resultant shift in the ratio of oscillation amplitudes is predicted using perturbation analysis and verified against numerical results obtained via parameter continuation. A physical realization of the mass sensing mechanism is proposed, in which the linear oscillator is represented by a periodically excited actuator/microcantilever assembly, the nonlinear oscillator is simulated in silico on a finite interval of time while driven by the periodic steady-state response of the linear oscillator, and a nonlinear root-finding algorithm is used to identify the input to the actuator that reproduces the sought, coupled, self-excited dynamics. The analysis shows that the sensor gain can be adjusted by appropriate tuning of the coupling stiffness without modifications to the physical components. Numerical results for two different actuator models demonstrate rapid convergence of the root-finding algorithm from a trivial initial solution guess over ranges of values of model parameters and added mass ratios.