标题： 扭振模态和悬臂及T型微悬臂的灵敏度分析 显示英文标题

标题： Mode shapes and sensitivity analysis of torsional vibrations in overhang- and T-shaped microcantilevers

摘要： 原子力显微镜（AFM）悬臂的扭转模式在广泛的灵敏测量中起着关键作用。 尽管它们很重要，但使用近似频率和模态形状来处理宽度变化的悬臂通常会导致理论模型与实验观察之间的差异。 在本研究中，我们提出了一种分析方法，以准确计算这些悬臂的模态形状和共振频率，包括高阶模态，然后我们推导了模态灵敏度。 我们的结果揭示了随着悬伸长度增加，模态形状和频率出现显著变化，模态形状显示出多个极大值。 此外，我们证明调整悬伸长度可以有效控制共振频率。 还建立了模态灵敏度与悬臂和表面之间耦合强度之间的关系，这与以前的实验结果一致。 这项工作为优化悬臂几何形状以在AFM应用中实现所需的频率响应提供了有价值的见解。 显示英文摘要

摘要： The torsional mode of atomic force microscope (AFM) cantilevers plays a crucial role in a wide range of sensitive measurements. Despite their importance, the use of approximated frequencies and mode shapes for width-varying cantilevers often results in discrepancies between theoretical models and experimental observations. In this study, we present an analytical approach to accurately calculate the mode shapes and resonance frequencies of these cantilevers, including higher-order modes, then we derive the modal sensitivity. Our results reveal distinct changes in mode shapes and frequencies as the overhang length increases, with the mode shapes showing multiple maxima. Furthermore, we demonstrate that tuning the overhang length provides effective control over the resonant frequency. The relationship between modal sensitivity and the coupling strength between the cantilever and the surface is also established, aligning with previous experimental findings. This work offers valuable insights for optimizing cantilever geometry to achieve desired frequency responses in AFM applications.