Page 135 - Mechanics of Microelectromechanical Systems
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122 Chapter 2
Solution:
By applying Castigliano’s displacement theorem, the deflection and
slope at point 2 can be calculated as:
which indicates that the compliances are:
and therefore, each of these compliances has the general form of the full-
length compliances given in Chapter 1, but they are calculated for half the
length. They can be expressed in terms of the compliances corresponding to a
microcantilever of length l as:
Returning to the generic microbridge of Fig. 2.39, the unknown reactions
and are first determined by applying Castigliano’s displacement
theorem and the zero deflection and zero slope boundary conditions at point
1. The reactions are of the form:
where the constants and are calculated as:
The coefficients of Eqs. (2.194) depend on the compliances of the individual
portions 1-2, 2-4 and 4-5 in the form:
