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5. Static response of MEMS 279
where:
Solution of Eq. (5.36), via Eqs. (5.37), gives the following value of the
temperature increase (which is embedded in both and
With the numerical values of this example, the temperature increment has a
value of
Example 5.8
A two bent beam thermal actuator, as the one sketched in Fig. 5.14 (a), of
specified geometry and material properties, has to be evaluated. Its output
displacement is determined optically, whereas the output force is measured
indirectly by means of the fixed-free constant cross-section beam, which is
positioned as shown in the same figure. Determine the Young’s modulus of
the microdevice, as well as the output force. The geometry of the bent beam
is: the geometry of the test beam is:
the coefficient of thermal expansion is
l/° and the temperature increase is
Solution:
According to the spring model of Fig. 5.14 (b), the force equilibrium
equation is:
where the subscript bb denotes the bent beam and the subscript b stands for
the beam dedicated to measuring the actuation force. The thermal actuation
force is determined by means of the bloc force and the free displacement,
according to Eqs. (4.9) and (4.8) in Chapter 4. Also the stiffness of one bent
beam is known – Eq. (3.18) in Chapter 3. The stiffness of the test beam is
simply:
