Page 207 - Mechanics of Microelectromechanical Systems
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194 Chapter 4
displacements can be formulated by considering the strain energy stored in
the two beams through bending and axial effects‚ and by applying
Castigliano’s displacement theorem. After determining the three reactions as
functions of and the system’s geometry‚ the rotation at point 2 can be
found similarly‚ and its equation is:
It has been assumed in Eq. (4.13)‚ as well as in all following equations of this
sub-section‚ that the two beams have identical cross-sections and are built of
the same material. The free displacement at point 2 is found to be:
The bloc force can be found by expressing first as a function of and
then taking This gives the bloc force as:
It is interesting to study how the length parameters and influence the
performance of the two-beam thermal actuator‚ for instance the free
displacement of Eq. (4.14)‚ as discussed in the following example.
Example 4.4
Analyze the free displacement of a two-beam actuator by expressing
and as fractions of the length The following geometric and material
values are known: E
= 130 GPa.
Solution:
Considering that (see Fig. 4.14) and that the short lengths
and are fractions of the long beam’s length namely:
