Page 251 - Mechanics of Microelectromechanical Systems

238 Chapter 4
and the underlying mechanism can be utilized in micro-scale sensing for
instance.

Example 4.13
A circular, circumferentially-clamped SMA membrane in martensitic
state is deformed through an external pressure such that a maximum central
deflection is reached. A temperature increase of is applied to the
membrane and the martensite transforms completely in austenite. Find the
maximum force that can be generated through this reversed transformation.
Consider that the membrane is defined by a radius and thickness
The elastic properties of the austenite and martensite are:
(after Otsuka and
Wayman [10]). Also consider that

Solution:
The maximum force that can be generated during the membrane’s
martensitic-austenitic transformation equals the force that is needed to
prevent any resulting deformation, and the stiffness of a clamped circular
plate that is acted upon by a force placed at the symmetry center
perpendicularly to the membrane plane is given in Eq. (1.231), Chapter 1. As
a consequence, the maximum (bloc) force becomes:

The flexural rigidities in austenitic and martensitic phase are:

By using the numerical values of this problem, the maximum force is found
to be of 0.206 mN.

8 BIMORPH TRANSDUCTION

8.1 Generic Formulation

Bimorphs are composed of two layers of different materials laid upon
each other as sketched in Fig. 4.51 (a). In general, one layer is active, in the
sense that it can deform axially upon application of a specific type of energy.
Because the two layers are sandwiched together, the free axial deformation
of the top layer is constrained by the bottom layer and, as a result, the
composite beam will bend. When the top layer shrinks, the resulting
deformed shape of the beam is the one shown in Fig. 4.51 (b). When the free