Parkin John D, Hähner Georg
EaStCHEM School of Chemistry, University of St. Andrews, North Haugh, St. Andrews, KY16 9ST, United Kingdom.
Rev Sci Instrum. 2011 Mar;82(3):035108. doi: 10.1063/1.3563724.
Micro- and nanocantilevers are increasingly employed as mass sensors. Most studies consider the first flexural mode and adsorbed masses that are either discretely attached or homogeneously distributed along the entire length of the cantilever. We derive general expressions that allow for the determination of the total attached mass with any mass distribution along the cantilever length and all flexural modes. The expressions are valid for all cantilevers whose flexural deflection can be described by a one-dimensional function. This approach includes the most common types of microcantilevers, namely, rectangular, picket, and V-shaped. The theoretical results are compared with experimental data up to the fourth flexural mode obtained from thermal noise spectra of rectangular and V-shaped cantilevers.
微纳悬臂梁越来越多地被用作质量传感器。大多数研究考虑的是一阶弯曲模式以及离散附着或沿悬臂梁全长均匀分布的吸附质量。我们推导了通用表达式，可用于确定沿悬臂梁长度具有任意质量分布以及所有弯曲模式下的总附着质量。这些表达式适用于所有弯曲挠度可用一维函数描述的悬臂梁。这种方法涵盖了最常见的微悬臂梁类型，即矩形、尖桩形和V形。将理论结果与从矩形和V形悬臂梁的热噪声谱获得的直至第四阶弯曲模式的实验数据进行了比较。
