Page 164 - Mechanical design of microresonators _ modeling and applications
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Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design
Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design 163
Figure 3.37 Resonant array with rectangular cross-section microcantilevers.
Figure 3.38 Resonant array with circular cross-section microcantilevers.
whereas for a circular cross-section microcantilever, the length-
frequency relationship is
4 Ed 2
l = 0.377 (3.180)
ȡ f 2
The plot of Fig. 3.39 shows the length as a function of frequency, ac-
cording to Eq. (3.179), for polysilicon with E = 150 MPa, and ȡ = 2300
3
kg/m and when the thickness t = 0.5 m.
As the figure indicates, the length decreases nonlinearly with the
resonant frequency increasing. If a given distance needs to contain
several microcantilevers, then the lengths of the microbridge network
need to follow the profile of the plot shown in Fig. 3.39. A more detailed
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