Page 55 - Mechanics of Microelectromechanical Systems
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42 Chapter 1
Example 1.10
Consider a quarter-circle fixed-free curved bar for which w = 0.1 R.
Calculate the compliance by considering that the beam is thick and
then compare the result with the one produced when considering that the
beam is thin.
Solution
For a thin curved beam, the compliance of interest is in this particular
case
For a thick beam, the same compliance is given in Eq (1.131). After carrying
out the required numerical calculations, the ratio between the compliance
calculated according to the thin beam theory and the same compliance
computed by means of the thick beam assumption is 0.999, which proves that
for the limit value w = 0.1 R, both theories provide similar predictions.
Example 1.11
Find the out-of-the-plane (z-direction) deflection of the free end 1
produced by the force acting about a direction perpendicular to
the plane of the free-fixed quarter-circle microbeam of Fig. 1.24. The radius
of the circle is and the cross-section is rectangular with
and The material is homogeneous with E = 150 GPa and
Figure 1.24 Out-of-the-plane loading of a curved beam
Solution
The deflection about the z-direction of point 1 can be found by using Eq.
(1.137) in the form:
