Nonlinear electromechanical and FSI modelling of piezoelectric AFM microcantilever dynamics in air and liquid environments

Piezoelectric microcantilevers are key components in atomic force microscopy (AFM), where their vibrational behaviour directly affects sensitivity, resolution, and measurement accuracy, particularly in fluid environments relevant to biological and chemical sensing. Despite extensive prior research, a systematic investigation of the geometrical effects of dual-layer piezoelectric configurations and a fully coupled electromechanical fluid–structure interaction (FSI) analysis based on realistic computational fluid dynamics (CFD) remain limited. This study presents a comprehensive three-dimensional finite-element framework to analyse the nonlinear electromechanical dynamics of piezoelectric AFM microcantilevers operating in both air and liquid environments. Geometrical nonlinearity is incorporated through large-deflection kinematics using the Green–Lagrange strain–displacement relations within a total Lagrangian formulation. First, air operation is examined through extensive parametric studies, systematically quantifying the influence of piezoelectric layer geometry (length, width, and thickness) across multiple single- and dual-layer configurations. Second, the model is extended to liquid operation through a fully coupled FSI formulation using CFD, enabling accurate representation of hydrodynamic damping and added mass effects. The numerical predictions show close agreement with published experimental and numerical results, validating both the structural and FSI frameworks. The results reveal distinct and configuration-dependent trends between air and liquid operation and provide quantitative design guidelines for optimising piezoelectric AFM microcantilevers for high-performance sensing in complex fluid environments.