Frequency Analysis and Liquid-Environment Sensing of Geometry-Dependent Microcantilevers Enabled by Supervised Learning

High Resolution Image Download MS PowerPoint Slide Microcantilever resonators underpin nanoscale imaging and sensing, yet their operation in liquid environments is fundamentally limited by fluid–structure coupling, added mass, and viscous damping. Accurate modeling is further complicated by practical geometries such as triangular-tipped cantilevers, which are often approximated as rectangular beams, reducing predictive reliability. Here, we develop an analytical–computational framework for triangular-tipped microcantilevers, enabling quantitative modeling and sensing in liquid environments, and validate it through numerical simulations and experiments in air and multiple liquids. The model combines first-order shear deformation theory with modified couple stress theory to capture size-dependent stiffness, while hydrodynamic loading is incorporated via added mass and damping to predict resonance frequency shifts and quality-factor variations. The framework shows strong agreement with experimental and numerical results across environments. Building upon this, we integrate supervised learning to infer liquid density and viscosity directly from resonance features, achieving accurate and robust predictions. This work establishes triangular-tipped microcantilevers as reliable resonant sensors in liquids and demonstrates the power of combining analytical mechanics with machine learning for high-fidelity fluid property estimation in applications such as AFM, microfluidics, and biosensing.