标题： 揭示悬臂梁扭转振动中具有悬臂和T形几何结构的模式形状复杂性和敏感性 显示英文标题

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

摘要： 原子力显微镜（AFM）悬臂的扭转振动对于高灵敏度测量至关重要，但现有变宽度悬臂的模型通常依赖于近似方法，导致与实验数据存在显著差异。 与以往研究不同，本工作引入了一种改进的分析框架，精确计算了悬臂梁的共振频率和模态形状，包括高阶模态，并通过针对性的实验对比进行了验证。 通过对悬臂长度系统性分析，我们揭示了之前未被报道的多峰值模态形状，并展示了如何通过几何调节可控地改变共振频率。 此外，我们建立了模态敏感性和悬臂-表面耦合强度之间的定量关系，为优化AFM悬臂性能提供了可行的设计原则。 我们的研究不仅使理论预测与实验观察相一致，还为调整悬臂几何形状以实现特定频率响应提供了实用指南，例如在纳米机械成像和表面特性测绘中的应用。 这项工作通过弥合理论模型与实际操作需求之间的差距，推动了下一代AFM探针的设计。 显示英文摘要

摘要： 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.