Page 336 - Mechanics of Microelectromechanical Systems
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5. Static response of MEMS 323
more appropriate for aluminum-type materials – Chen and Lui [6]. In MEMS
devices, however, the inelastic buckling is not desirable, and redesign has to
be performed when a component is plausible to buckle inelastically.
Example 5.21
A guided-fixed beam-column, as the one sketched in Fig. 5.56 (a), which
is intended to function as an out-of-the-plane actuator, is designed by mistake
such that Take the necessary measures in order for the beam
column to operate reliably as an actuator. The material of the
microcomponent cannot be changed and the length is also specified.
Solution:
Because the beam-column will eventually buckle inelastically, as
shown in Fig. 5.57, and this is an undesired condition. For elastic buckling it
is necessary that the redesigned component have a slenderness ratio larger
than the proportionality limit. By considering a rectangular cross-section
defined by w and t (w being the in-plane dimension, and w > t), the
slenderness ratio in the initial design can be expressed as:
when taking into account that:
Obviously, the new slenderness ratio (of the redesigned microactuator) is
expressed similarly as:
and the intention is that:
in order to insure that the new slenderness ratio is at least equal to the
proportionality limit so that buckling takes place in the elastic domain.
Combination of Eqs. (5.163), (5.165) and (5.166) results in the following
relationship:
