Abstract

The mathematical model of an AFM nonuniform probe in the modified couple stress theory is derived here. The analytical method is proposed to design the configuration of the AFM probe satisfying the integer-multiples relation among frequencies. The varying cross-section of the probe is tuned to match the specific requirement. One discovers two similarity conditions such that the integer-multiples relation is kept in spite of the size-dependency parameter. Moreover, the relations among the natural frequencies, the effective spring constant and the geometry parameters are discovered. The specific frequencies and spring constant can be obtained by tuning the probe parameters via the relations.

摘要

在此导出了修正耦合应力理论中 AFM 非均匀探针的数学模型。提出了分析方法来设计满足频率之间整数倍关系的AFM探头的配置。调整探头的不同横截面以匹配特定要求。人们发现了两种相似性条件，使得整数倍数关系保持不变，尽管有大小相关参数。此外，还发现了固有频率、有效弹簧常数和几何参数之间的关系。具体频率和弹簧常数可以通过调整探头参数来获得。