Vibration Analysis and Sensitivity Analysis of Semi-Submerged Multilayer Piezoelectric Microcantilever

The growing development of nanobiotechnology and its applicability resulted in a wider range of use of Microcantilevers (MCs) in liquid. Considering the applications of piezoelectric MCs in the microelectromechanical systems and Atomic Force Microscope (AFM), as well as the high performance of these beams, this article investigates the vibrating behavior of multilayer piezoelectric MCs with geometric discontinuity in liquid environment. Due to the extreme complexity of hydrodynamic forces introduced to MCs, this force may reduce their accuracy. As a result, the MC was considered to be semi-submerged in the liquid medium to reduce the effect of hydrodynamic force. In addition, to reduce the effect of hydrodynamic force on vibrating behavior of the MC, sensitivity analysis was performed on its geometric dimensions to obtain the optimal dimensions, aiming at minimizing the effect of this force. The differential equation of motion was derived using the Euler–Bernoulli theory and the Lagrange method. The hydrodynamic force was exerted on the MC through the sphere string model. The Simulation results indicated that due to reducing resonance frequency variations in the third vibrating mode, the effect of hydrodynamic force on vibrating motion is minimized in this mode and considered as the optimal vibrating mode among the first three modes. The sensitivity analysis results showed that the MC length and piezoelectric layer were geometric parameters with the greatest effect on frequency sensitivity of MC, which should be considered in semi-submerged piezoelectric MC design.