Revealing Modeshape Complexity and Sensitivity in Torsional Vibrations of Microcantilevers with Overhang- and T-shaped Geometries

TL;DR

This study develops a precise analytical model for torsional vibrations in complex microcantilever geometries, validated by experiments, revealing new mode behaviors and guiding optimized AFM probe design for enhanced sensitivity.

Contribution

It introduces a refined analytical framework for overhang- and T-shaped microcantilevers, accurately predicting resonance frequencies and mode shapes, including higher-order modes, with experimental validation.

Findings

Identification of multi-maxima mode shapes due to overhang effects

Demonstration of geometric tuning to shift resonant frequencies

Establishment of a relationship between modal sensitivity and surface coupling

Abstract

The torsional vibration of atomic force microscope (AFM) cantilevers is critical for high-sensitivity measurements, yet existing models for width-varying cantilevers often rely on approximations that lead to significant discrepancies with experimental data. Unlike prior studies, this work introduces a refined analytical framework to precisely compute resonance frequencies and mode shapes, including higher-order modes, for overhang- and T-shaped microcantilevers, validated through targeted experimental comparisons. By systematically analyzing the effects of overhang length, we reveal previously unreported multi-maxima mode shapes and demonstrate how geometric tuning can controllably shift resonant frequencies. Furthermore, we establish a quantitative relationship between modal sensitivity and cantilever-surface coupling strength, providing actionable design principles for optimizing AFM cantilever performance. Our results not only reconcile theoretical predictions with experimental observations but also offer practical guidelines for tailoring cantilever geometry to achieve specific frequency responses in applications such as nanomechanical imaging and surface property mapping. This work advances the design of next-generation AFM probes by bridging the gap between analytical models and real-world operational demands.