Sensitivity analysis of piezo-driven stepped cantilever beams for simultaneous viscosity and density measurement

Abstract

This paper presents a study on the sensitivity analysis of a smart sensing system for simultaneous measurement of a viscous fluid's viscosity and density. The proposed system is based on a piezo-driven Euler–Bernoulli (cantilever) beam. Three stepped cantilever beams of varying widths were fabricated to investigate the sensitivity in relation to cantilever design. Mathematical modeling was first derived based on the Stokes' law and Euler–Bernoulli equations. Based on the modeling, numerical simulation was conducted and the vibration spectrums of cantilever beams with viscous fluid loading were analyzed. Results show that the resonant frequency and vibration amplitude of the proposed sensing system is sensitive to both the dynamic viscosity and the density of the sample fluid. To verify the numerical results, laboratory experiments were performed. The experimental results are congruent with the numerical results Furthermore, the two-step cantilever beam proved to have the highest sensitivity for viscosity measurement when compared with the other configurations. The proposed sensing system can also be downsized into the micro domain for high temperature engine oil viscometers for use in the automobile industry or can be applied to early age concrete curing process monitoring.