Mass identification of multiple particles on a doubly clamped resonator

The shift of resonant frequencies is the working mechanism of a mass resonator sensor. The shift is due to the adsorption of particles, which can change the mass, stiffness and damping of the sensor. Based on the Timoshenko beam model, an analytical model and mathematical solution are proposed to explain the frequency shifts due to the adsorption of multiple particles. The model shows a better accuracy in the scenarios of the high order resonance, the vibration in the viscous environment and under high tension. The inverse problem of identifying multi-particle mass is solved by an iteration algorithm, whose performance is also evaluated for the measured noise and adsorption areas. The mass identification of multiple particles shows a better sensitivity and robustness than that of single particle, which is somewhat surprising but beneficial to mass sensing. The results in this study provide a theoretical basis for the mass identification of multiple particles and are of some help to the practical application