Dynamic behavior of Resonant Piezoelectric cantilevers partially immersed in liquid

Resonant Piezoelectric-excited Millimeter-sized Cantilevers (PEMC), has attracted many researchers' interest in the applications such as liquid level and density sensing. As in these applications, the PEMC are partially immersed in liquid, an appropriate analytical model is needed to predict the dynamic behavior of these devices. In this work, a PEMC has been fabricated for liquid level sensing. An analytical model based on Euler-Bernoulli theory and energy method is developed and applied to evaluate the performance of this device with respect to different tip immersion depth. To validate this model, the theoretical results are compared with the experimental results for the tip immersion depth from 0.5 mm to 9 mm in water. The simulation results are in almost good agreement with experimental data. The difference in natural frequency obtained by the theoretical model for different immersion depth remains less than 8%. The linear region of the natural frequency shift versus immersion depth has been identified to be from the depth of 9 to 11 mm.