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

doi:10.1007/s11465-014-0286-x

Front. Mech. Eng.

2014, Vol. 9

Issue (1) : 50-57 https://doi.org/10.1007/s11465-014-0286-x

RESEARCH ARTICLE

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

Qi XIA^1,^*(

),Tao ZHOU¹,Michael Yu WANG²,Tielin SHI¹

1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, China

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Abstract

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.

Keywords atomic force microscopy cantilever probe eigenfrequency optimization

Corresponding Author(s): Qi XIA

Issue Date: 16 May 2014

Cite this article:

Qi XIA,Tao ZHOU,Michael Yu WANG, et al. Shape and topology optimization for tailoring the ratio between two flexural eigenfrequencies of atomic force microscopy cantilever probe[J]. Front. Mech. Eng., 2014, 9(1): 50-57.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0286-x
https://academic.hep.com.cn/fme/EN/Y2014/V9/I1/50

Fig.1 Design velocity and propagation of a free boundary

Fig.2 Design problem

Fig.3 Initial design and the optimal design. (a) Initial design; (b) optimal design

Fig.4 Transverse displacement w of flexural eigenmodes of the optimal design. (a) The first flexural eigenmode; (b) the third flexural eigenmode

Fig.5 Convergence history

Fig.6 Intermediate results of the optimization. (a) Step 100; (b) step 200; (c) step 300; (d) step 400

Tab.1 Numerical results of the optimization (f₁: the first flexural eigenfrequency; f_k: the k-th flexural eigenfrequency; A: area of the cantilever)

Fig.7 Design problem

Fig.8 Initial design and the optimal design. (a) initial design; (b) optimal design

Fig.9 Transverse displacement of flexural eigenmodes of the optimal design. (a) The first flexural eigenmode; (b) the second flexural eigenmode

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