Shape and topology optimization for tailoring the ratio between two flexural eigenfrequencies of atomic force microscopy cantilever probe

In an operation mode of atomic force microscopy that uses a higher eigenmode to determine the physical properties of material surface, the ratio between the eigenfrequency of a higher flexural eigenmode and that of the first flexural eigenmode was identified as an important parameter that affects the sensitivity and accessibility. Structure features such as cut-out are often used to tune the ratio of eigenfrequencies and to enhance the performance. However, there lacks a systematic and automatic method for tailoring the ratio. In order to deal with this issue, a shape and topology optimization problem is formulated, where the ratio between two eigenfrequencies is defined as a constraint and the area of the cantilever is maximized. The optimization problem is solved via the level set based method.