Page 92 - Mechanics of Microelectromechanical Systems
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2. Microcantilevers, microhinges, microbridges 79
By coupling Eqs. (2.36) through (2.40) it is possible to determine the amount
of deposited mass as well as its in-plane position defined by and
Example 2.4
Determine the added mass as well as its position and on a
variable cross-section microcantilever when the tip slopes and and the
deflection are known.
Solution:
When the cross-section of the microcantilever is variable, the tip slope
(which is given in Eq. (2.35) for a constant cross-section) can be found by
means of Castigliano’s displacement theorem as:
where:
is the compliance of the microcantilever portion which is comprised between
the point of application of the deposited mass and the fixed root. In a similar
manner, the tip deflection can be expressed as:
where the new partial compliance is:
The torsion-related tip slope is expressed as:
with the partial torsional compliance being:
