Resonant behavior study of PZT sensor in liquid using PSO method

Resonant Piezoelectric-excited Millimeter-sized Cantilevers (PEMC), has attracted many researchers' interests 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 designed and fabricated for liquid level sensing. An analytical model is developed and applied to evaluate the behavior of this device with respect to different tip immersion depths. To validate the proposed model, the theoretical results are compared with the experimental results for the tip immersion depths varying from 5 mm to 15 mm in water for two different resonant modes. A slight deviation between theoretical and experimental model have been observed. To justify the deviations, uncertain parameters and also hydrodynamic force's correction factor have been considered in modeling. This correction factor is introduced in theoretical modeling order to achieve a better estimation of the effect of immersion depth variation on the hydrodynamic force. To determine these parameters using experimental results, Particle Swarm Optimization (PSO) method is utilized. Applying this method, the deviation of theoretical results from experimental data is being significantly reduced. The results show that the uncertain parameters have negligible effect on the natural frequency shift of the PEMC in different immersion depths and on the contrary the hydrodynamic force's correction factor affects it drastically. It is concluded that to improve resonant behavior modeling of the PEMC partially immersed in liquid, for different immersion depths, an appropriate estimation of liquid force is required by insertion of hydrodynamic correction factor.