Page 153 - Mechanical design of microresonators _ modeling and applications

0-07-145538-8_CH03_152_08/30/05

Microhinges and Microcantilevers: Lumped-Parameter Modeling and Design

152 Chapter Three
components, as the case is with the majority of MEMS, the torsional
moment of inertia is
3
wt i
I = 3 (3.136)
ti
4
It has also been shown (see Lobontiu, for instance) that the equivalent
mechanical moment of inertia J t,e is calculated as
J t
J t,e = 3 (3.137)

where J t is the mechanical moment of inertia of the whole multimorph
and can be calculated as

n
J = ™ J + m (z í z ) 2 (3.138)
t ti i i C
i =1
The mechanical moment of inertia of the ith component taken with re-
spect to its central axis is

2
2
lwt ȡ (w + t )
i
i i
J = (3.139)
ti 12
The distance positioning the central axis of the ith component mea-
sured from the multimorph lowest layer (layer n), as suggested in
Fig. 3.30, is
t i n
z = 2 + ™ t k (3.140)
i
k = i +1

z

t1

z1
ti
zi zi
tn zn
w
Figure 3.30 Cross section of sandwich bar with main geometry parameters for torsional
resonant frequency calculations.

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.