Characterization of higher-order resonant cantilevers for density determination in different flowing liquids

This study investigates the sensing characteristics of micromachined electromagnetic cantilevers vibrating at different resonance orders and under static or flowing liquid immersions. The cantilever is designed with a wide-plate structure, which contributes to the modal optimization for basic and higher-order torsions. The fluid-structure interaction is used to analyze the parameterized expressions of the density and its changing sensitivity based on the cantilever's flexural and torsional vibrations. They have successfully clarified the comprehensive factors that influence the density measurement performance. The study shows that the analytical predictions for the density changing sensitivity agree well with the experimental results. The experiments prove that the cantilever under flowing immersion appears significantly degraded in its density measurement accuracy. Higher mode and shorter length enable the cantilever to respond better density sensing behaviors under flowing immersion. These results here can be further generalized to guide the optimal design of cantilever-based resonators in flowing liquid monitoring.