Page 101 - Mechanics of Microelectromechanical Systems
P. 101
88 Chapter 2
Again, the stiffnesses corresponding to bending about the z-axis can be
determined by inverting the compliance submatrix, Eq. (2.6), containing the
terms of Eqs. (2.75), (2.76) and (2.77).
The axial compliance is:
and the torsional compliance for a very thin cross-section (t << w) is:
The axial- and torsional-related stiffnesses are the algebraic inverses of the
corresponding compliances of Eqs. (2.78) and (2.79), respectively.
2.2.4.2 Elliptically-Filleted Design
The right elliptically-filleted microcantilever and the defining geometric
parameters are sketched in Fig. 2.15. The length of the microcantilever is
equal to the longer semi-axis a, whereas the height of the two filleted areas is
equal to the length of the other semi-axis b, but the design with the reversed
axes is also possible.
The variable width for this design is:
The compliances corresponding to bending about the sensitive axis are:
