Research Papers

Simulation of Micromechanical Measurement of Mass Accretion: Quantifying the Importance of Material Selection and Geometry on Performance

[+] Author and Article Information
Michael James Martin

Department of Mechanical Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: martinm2@asme.org

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 11, 2012; final manuscript received September 25, 2013; published online November 26, 2013. Assoc. Editor: Steven W Shaw.

J. Vib. Acoust 136(2), 021003 (Nov 26, 2013) (7 pages) Paper No: VIB-12-1098; doi: 10.1115/1.4025842 History: Received April 11, 2012; Revised September 25, 2013

Micro- and nanomechanical resonators operating in liquid have been used to measure the change in the mass of either cells or functionalized surfaces attached to the resonator. As the system accretes mass, the natural frequency of the system changes, which can be measured experimentally. The current work extends methods previously developed for simulation of an atomic force microscope operating in liquid to study this phenomenon. A silicon cantilever with a 10 micron width, an 800 nm thickness, and a length of 30 microns was selected as a baseline configuration. The change in resonant frequency as the system accretes mass was determined through simulation. The results show that the change in natural frequency as mass accretes on the resonator is predictable through simulation. The geometry and material of the cantilever were varied to optimize the system. The results show that shorter cantilevers yield large gains in system performance. The width does not have a large impact on the system performance. Selecting the optimal thickness requires balancing the increase in overall system mass with the improvement in frequency response as the structure becomes thicker. Because there is no limit to the maximum system stiffness, the optimal materials will be those with higher elastic moduli. Based on these criteria, the optimum resonator for mass accretion measurements will be significantly different than an optimized atomic-force microscopy (AFM) cantilever.

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Fig. 1

Resonator configuration

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Fig. 4

Displacement versus frequency for unloaded silicon resonators with varying lengths

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Fig. 5

Gain versus frequency for unloaded silicon resonators with varying lengths

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Fig. 6

Frequency shift versus accreted mass for silicon resonators with varying lengths

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Fig. 7

Gain versus frequency for unloaded silicon resonators with varying widths

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Fig. 8

Frequency shift versus accreted mass for silicon resonators with varying widths

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Fig. 9

Gain versus frequency for unloaded silicon resonators with varying thicknesses

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Fig. 10

Frequency shift versus accreted mass for silicon resonators with varying thicknesses

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Fig. 11

Displacement versus frequency for unloaded resonators with varying materials

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Fig. 12

Gain versus frequency for unloaded resonators with varying materials

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Fig. 13

Frequency shift versus accreted mass for resonators with varying materials




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