Page 340 - Mechanics of Microelectromechanical Systems
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5. Static response of MEMS 327
Figure 5.60 Equivalent loading of the pinned-pinned bent beam
The deformation produced through bending by the action of the force can
simply be found by integrating the following differential equations:
and by using the appropriate boundary conditions that are zero deflections at
points 1 and 3‚ as well as equal deflections and equal slopes at point 2. It can
be shown that the total offset of the deformed beam is:
where:
By using Eqs. (5.171) and (5.181)‚ it is found that the strain energy is equal
to:
The work done by the axial force is:
By equating the strain energy U to the work W‚ according to the energy
principle‚ gives the expression of the critical force:
