Page 171 - Mechanics of Microelectromechanical Systems
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158 Chapter 3
Figure 3.28 Short leg’s length as a function of the long leg’s length
Example 3.10
Compare the total axial stiffness of a serpentine spring which has 5
linearly-scaled units to the axial stiffness of another serpentine spring which
contains 5 identical units. The width of the third (middle) unit in the scaled
version is equal to the width of the units in the other design, which is
Assume the two configurations are built of the same material and have
identical constant rectangular cross-sections. The legs are defined by
and
Solution:
The total stiffness of each configuration is given by the rule of series
connection (which is also treated in Chapter 5) and therefore its expression is
determined as:
For the configuration with identical units the, factors of Eq. (3.85) are
identical, and can be calculated by inverting the compliance of Eq.
(3.75) with the appropriate length For the scaled version, one needs to
calculate the length for each of the units. It is known that the length of the
unit in the middle of the second design is equal to the length of the identical
units in the first design, namely.
The lengths of the other four units can be calculated with the aid of Fig. 3.26
as:
