Page 82 - Mechanics of Microelectromechanical Systems

2. Microcantilevers, microhinges, microbridges 69
the lumped-parameter axial, torsion and bending compliances/stiffnesses of
fixed-free, constant rectangular cross-section straight and curved
micromembers. The procedure followed in Chapter 1 – based on Fig. 1.18 –
also applies here, where the straight member is of variable cross-section. The
six degrees of freedom at the free end, as shown in Fig. 1.18, can formally be
grouped into the ones generated by bending about the sensitive axis (the y-
axis), namely: and bending about the other symmetry axis: and
axial deformation, and torsion, It has also been shown in Chapter 1
that the static response of a microcantilever can be formulated based on the
lumped-parameter model, in one of the two equivalent forms:

where:

is the displacement/deformation vector at the free end,

is the forcing vector at the same end, and:

is the compliance matrix whose bending-related sub-matrices are:

and