Accurate calibration of the flexural spring constant of microcantilevers is crucial for sensing devices, microactuators, and atomic force microscopy (AFM). Existing methods rely on precise knowledge of cantilever geometry, make significant simplifications, or require potentially damaging contact with the sample. Here, we develop a simple equation to calculate the flexural spring constants of arbitrarily shaped cantilevers in fluid. Our approach, verified here with AFM, only requires the measurement of two resonance frequencies of the cantilever in air and in a liquid, with no need for additional input or knowledge about the system. We validate the method with cantilevers of different shapes and compare its predictions with existing models. We also show how the method's accuracy can be considerably improved, especially in more viscous liquids, if the effective width of the cantilever is known. Significantly, the developed equations can be extended to calculate the spring constants of the cantilever's highe...

中文翻译：

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确定粘性环境中任意形状悬臂的弹簧常数

微悬臂梁弯曲弹簧常数的准确校准对于传感设备、微致动器和原子力显微镜 (AFM) 至关重要。现有方法依赖于对悬臂几何形状的精确了解，进行了显着的简化，或者需要与样品进行潜在的破坏性接触。在这里，我们开发了一个简单的方程来计算流体中任意形状悬臂的弯曲弹簧常数。我们的方法在这里用 AFM 验证，只需要测量悬臂在空气和液体中的两个共振频率，不需要额外的输入或有关系统的知识。我们使用不同形状的悬臂验证该方法，并将其预测与现有模型进行比较。我们还展示了如何显着提高该方法的准确性，尤其是在更粘稠的液体中，如果悬臂的有效宽度已知。重要的是，开发的方程可以扩展到计算悬臂高...