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248 Chapter 4
The change in temperature and the subsequent phase transformation from
martensite to austenite sends the operation point from the curve
corresponding to the martensitic SMA, with lower Young’s modulus, to the
curve representing the bending moment-curvature characteristic for the SMA
in the austenitic state, where Young’s modulus is larger. For the latter state,
the curvature is:
where, again, the bending rigidity is calculated by Eq. (1.180), Chapter 1, by
taking instead of
8.6 Bimorph with Dissimilar-Length Components
The bimorph configurations discussed thus far had identical lengths of
their components. There are also situations where one of the two layers is
shorter than the other. Figure 4.55 sketches such a design where the two
layers do not overlap completely. As shown previously, it is possible to
determine the bending moments M that are generated through induced strains
and act at the ends of the shorter layer, which mark the boundaries of the
overlapping region. It has also been shown in Chapter 1 that an equivalent
bending rigidity can be calculated for the length As a consequence,
it is possible to quantify the free displacement and the bloc force of this type
of actuator at its free end.
Figure 4.55 Bimorph with dissimilar-length layers
The free displacement, for instance, is given by the equation:
where the bending moment M is given in Eq. (4.135) and the equivalent
rigidity can be calculated as shown in Eq. (1.180) of Chapter 1. The force
