Investigation of Nonlinear Vibration Behavior of Piezoelectric Micro-Beam Interacting with Spherical Nano Particles

Today, piezoelectric micro-beams are widely used in atomic and friction force microscopies, thermal scanning microscopy, and biomass measurement due to their flexible structure, sensitivity to molecular and atomic forces, and very fast response. Due to the small displacements of these micro-beams, their complete vibrating analysis and studying their behavior can play a key role in their measurement precision and optimal design. For this reason, first the numerical Runge-Kutta method (based on the discontinuous beam model) as well as the finite element method was employed to solve the differential equation governing the piezoelectric micro-beams motion by considering geometrical discontinuities. Then, the sensitivity analysis was conducted to determine the effects of each micro-beams geometric parameter on the main parameters of the vibratory motion. The sensitivity analysis was conducted using Sobol method which is based on the output data variance. According to the obtained results, both the discontinuous cantilever model and the finite element model exhibited acceptable accuracy in calculating the natural frequency as well as the resonance amplitude of this type of micro-beams. Also, the results obtained from the sensitivity analysis showed that the first mode of the vibratory MC motion was the most suitable mode for nanoparticle surface topography.