Page 118 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 105

where the compliances of Eqs. (2.138) are calculated as:

The superscripts (1) and (2) in Eqs. (2.139), (2.140) and (2.141) indicate the
first component and the second component, respectively, whereas the same
numbers in the subscripts indicate the point where the respective compliance
has been calculated. In other words, indicates the linear compliance
of the component at the tip (the first component), calculated at point 1 and
considering that the member 1-2 is fixed at 2. Similarly, represents
the linear compliance of the component at the root of the compound
microcantilever (component number 2), calculated at point 2 with respect to
the fixed point 3. Having found the overall compliances of the compound
microcantilever, the corresponding stiffnesses are simply determined by
inversion of the symmetric compliance matrix, which consists of
and as shown in Eq. (2.127), for instance.
It is also simple to demonstrate that the overall axial and torsional
compliances are the sums of the corresponding individual compliances,
namely:

and

One of the simplest two-component microcantilevers is shown in Fig.
2.27, where two rectangular cutouts have been removed symmetrically from
a rectangular microcantilever.