Page 213 - Mechanical design of microresonators _ modeling and applications

0-07-145538-8_CH04_212_08/30/05

Microbridges: Lumped-Parameter Modeling and Design

212 Chapter Four
y

l/2
fixed fixed
α

w2 w1
x w

x

l
Figure 4.24 Geometry of a simplified doubly trapezoid microbridge.

(63 + 193c ) ȡtw l
w
2 1
m = (4.151)
b,e 315
and the resulting bending-produced resonant frequency is
10.247(1í c )t E ln c w
w
Ȧ b,e = 2 × (4.152)
l ȡ(63c +193) (c +1)ln c í 2(c í1)
w
w
w
w
1
The torsional stiffness is
3
2G(c Ì 1)t w 2
w
k = (4.153)
t,e 3l ln c w
1
The lumped-parameter inertia fraction which is dynamically equiva-
lent to the free torsional vibrations of the distributed-parameter
microbridge is
2
{28(11c +5)t + 35 + c (87
w
w
2
+ c (141 + 185c )) w } ȡtw l (4.154)
w
2 1
1
w
J =
t,e 5040
The torsional resonant frequency is

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