Page 224 - Mechanical design of microresonators _ modeling and applications

0-07-145538-8_CH04_223_08/30/05

Microbridges: Lumped-Parameter Modeling and Design

Microbridges: Lumped-Parameter Modeling and Design 223
13
12

11
Length [mm] 10

9
8
7
6
0 5000 10000 15000 20000

Resonant frequency [Hz]
Figure 4.35 Length of constant-cross-section bridge in terms of resonant frequency.

g
w lmin

geometric
envelope
1 max

microbridges

p
x
Figure 4.36 Microbridge network with nonlinearly varying length.

The relatively long bridges which are necessary at small resonant
frequencies can be replaced by fixed-free beams (cantilevers) or by
utilizing notches in a bridge; both solutions will enable us to obtain
resonators of smaller lengths. The length profile of Fig. 4.35, which has
been plotted based on Eq. (4.179), is also shown in Fig. 4.36.
Another microbridge network variant can be constituted of cylin-
drical wires, as sketched in Fig. 4.37.

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com)
Copyright © 2004 The McGraw-Hill Companies. All rights reserved.
Any use is subject to the Terms of Use as given at the website.