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74 Chapter 2
Figure 2.5 is the plot of this error function in terms of the tip deflection
and slope when and It can be
seen that the errors can be as high as 75% for large tip deflections and small
slopes.
2.2.2 Constant Rectangular Cross-Section Design
The absolute values of the stiffnesses that define the out-of-the-plane
bending about the sensitive axis (the y-axis in Fig. 2.3) have been given in
Chapter 1 and are written here as:
Similarly, the magnitudes of the stiffnesses that define the bending about the
z-axis are:
The axial stiffness is:
The torsion stiffness in the case where the thickness is considerably smaller
than the width (t << w) is:
Example 2.2
Compare the stiffnesses that characterize the bending about the sensitive
axis (the y-axis) to the other pertinent stiffnesses of a constant rectangular
cross-section microcantilever.
Solution:
The length l and width w of a microcantilever are expressed in terms of
the thickness t as:
