Page 56 - Mechanics of Microelectromechanical Systems

1. Stiffness basics 43

because the only load is
The compliance of Eq. (1.165) can be determined from Eq. (1.163) in the
following form:

The moments of inertia are:

and E and G are related according to Eq. (1.23). By using the numerical
values given in this example, it is found that the out-of-the-plane deflection is

6. COMPOSITE MEMBERS

Many structural microcomponents are built in a composite manner by
depositing layers of different materials on a structural component. A thin
piezoelectric layer might be attached to the structural layer of a
microcantilever, in order to achieve actuation or sensing purposes for
instance. There are also cases where members of different cross-sectional
and/or material properties are fabricated in a serial manner in beam-type
microcomponents that are designed for various transduction purposes. Both
cases will be analyzed next by focusing on one-dimension (line) members.

6.1 Sandwiched Members

Figure 1.25 (a) shows the cross-section of a sandwich beam consisting of
two different materials, having the elastic modulii and for instance.
Figures 1.25 (b) and (c) picture the strain and stress variations over the height
of the compound cross-section as produced through bending. The two layers
have different thickness, and and identical widths w – but this is not a
necessary condition. In such instances, stiffness properties can be formulated
that are equivalent to the real situation, by utilizing the stiffness or
compliance equations that have been derived for homogeneous cross-sections.
The response to bending, axial loading and torsion will be addressed next.