Page 119 - Mechanics of Microelectromechanical Systems
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106 Chapter 2
Example 2.12
Determine the stiffness that are related to bending about the sensitive
axis (which passes through the anchor) to axial deformation and torsion for a
microcantilever which if formed of two constant rectangular cross-section
segments, as sketched in Fig. 2.27. It is known that
and (the sensitive plate is denoted by 1 and the thinner
microcantilever by 2).
Figure 2.27 Microcantilever formed of two rectangular components
Solution:
The individual compliances of the two portions are:
for the free end segment and:
for the root segment. The overall compliances are found by using Eqs.
(2.139) through (2.143), which enables formulation of the 2 x 2 compliance
matrix. The stiffness matrix is determined by inversion of the compliance
matrix and its terms are:
