Page 37 - Mechanics of Microelectromechanical Systems
P. 37
24 Chapter 1
Figure 1.16 Fixed-guided beam
At the same time, the deflection can be expressed by means of
Castigliano’s displacement theorem, Eq. (1.70), as:
The bending moment at the generic position of abscissa x is:
It can be seen in Eq, (1.75) that the partial derivative of in terms of is
x. As a consequence, Eq. (1.74) permits solving for the unknown
namely:
In order to find the slope at midspan, a dummy moment is artificially
applied at point 2 in order to enable performing calculations by means of
Castigliano’s displacement theorem in the form:
The bending moment will have two different equations one for each of the
intervals 1-2 and 2-3, namely:
