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Microbridges: Lumped-Parameter Modeling and Design
186 Chapter Four
This transform is mainly useful when we are carrying out stiffness
calculations for microbridges which are formed of a single geometric
curve (profile) and which possess a transverse symmetry axis.
The subscript f is used here to denote the full-length microhinge
whereas for the half portion between points 2 and 3 in Fig. 4.14, no
additional subscript notation is utilized. The following equations can be
written in terms of bending compliances:
2
/
l 2 l 2 2 l 2 l C
C l, f x dx = x dx + x dx = r +2C l
=
/
0 EI y 0 EI y l 2 EI y 2
l l 2 l (4.64)
/
c, f xdx xdx xdx
C = = + = lC r
/
0 EI y 0 EI y l 2 EI y
2C c
C r, f = l
Equations (4.64) have been derived by applying the two compliance
transforms of Chap. 3. By solving the first two of Eqs. (4.64), the two
compliances that correspond to one-half the microhinge of Fig. 4.14 are
determined to be
2C l, f í lC c, f C c, f
C = C = (4.65)
l r
4 l
It can also be shown that the torsional compliance of the segment 2-3
can be expressed in terms of the compliance of the full-length micro-
hinge as
C t, f
C = (4.66)
t 2
4.4.2 Generic formulation for single-profile
(basic shape) microbridges
As was the case with constant-cross-section microbridges, only a half-
model of a variable-cross-section microbridge is analyzed, provided
there is transverse symmetry of the design, which means that one-half
of the microbridge is mirrored-identical to the other half. Figure 3.7,
which was used for symmetric microcantilevers, is also valid for this
derivation, and the generic half-bridge model of Fig. 4.4 is as well. The
assumption is made with this model that the microbridge width is
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