Page 320 - Mechanics of Microelectromechanical Systems
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5. Static response of MEMS 307
units and the input stiffness of the middle unit need to be small in order to
produce large output displacements.
6. LARGE DEFORMATIONS
There are MEMS devices which are designed to operate under conditions
of large deformations/displacements in order to amplify their output
capabilities.
Figure 5.42 Rigid bar with one end pinned and a spring and a load at the other end
While the separation between small and large displacements is rather
flexible, the mathematical description and solutions of the two theories are
quite different. The small-displacement theory considers that the loading and
resulting deformations/displacements of a microcomponent are independent
and can be superimposed linearly. The large-displacement theory is non-
linear, and effects of different loads do combine and affect each other and,
together, they affect the deformed state of a MEMS component. In many
instances, an originally non-linear mathematical model can be linearized,
especially when the deformations are small, as shown in the example of Fig.
5.42, where the axial force produces an angular rotation of the pinned bar
of length l, because of an initial misalignment from the horizontal position.
The moment equilibrium equation is:
The following small-displacement approximations are used:
which transform Eq. (5.121) into:
