Semi-analytical modeling of a partially wetted resonant mass sensor operated in a low-loss localized eigenmode

Abstract

We present a semi-analytical model, describing the mechanical behavior of a partially wetted low-loss microresonator, designed for mass sensing applications in both gaseous and liquid environment. In the course of this detailed modeling, realistic boundary conditions have been implemented, and the impact of the support structure on the spectral behavior of the resonator has been investigated. We proof the existence of localized eigenmodes, in spite of the diminishing clamping of the resonator, considering higher modes of the resonator/support system. The quality factor of the partially wetted resonator was evaluated including various types of damping mechanisms. The quantification of the detection limit is the key to optimize the geometry of this sensor type.

Mode Localization and Eigenfrequency Curve Veerings of Two Overhanged Beams

“…As shown in Figure 1 , overhang is a mechanical sledge shared by two or several (sub)structures [ 34 , 35 , 36 ]. Overhang physically couples the (sub)structures and leads to the eigenfrequency veering and mode localization, which has been used as an effective mechanism to increase the sensitivity of mass sensing [ 35 , 36 , 37 , 38 ]. Furthermore, a veering locus also (approximately) corresponds to the maximum shift of an eigenfrequency [ 37 ], which is a much sought-after property in a mass resonator sensor [ 26 , 27 , 28 ].…”

“…Due to their simple design, overhanging structures are an important type of resonator structure [ 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ]. Various numerical methods have been used to study the mode localization and eigenfrequency veering of the overhanging structures.…”

“…The effects of the overhang geometry on the veering and mode localization are systematically studied. This comprehensive study should be of some help to the design of the overhanging resonator structures [ 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 ]. Recently, Kasai et al [ 46 ] proposed an efficient method called “virtual coupling”, which can effectively change the coupling strength of a system through a nonlinear feedback scheme.…”