Page 63 - Mechanics of Microelectromechanical Systems
P. 63
50 Chapter 1
where i = 1, 2. If the stiffness of the compound beam 1-3 were to be
calculated by the rule that applies to serially-connected springs (this aspect
will be treated in more detail in Chapter 5), then it would be found by means
of the equation:
and its value would be:
However, if one calculates the free end’s deflection by means of
Castigliano’s displacement theorem, the real stiffness is:
where the denominator is:
It can be seen that the combined Eqs. (1.197) and (1.198) are not identical to
Eq. (1.196), and therefore the stiffness of the compound beam of Fig. 1.27
cannot be solved by following the simple rule that applies to springs.
Similarly, the other two bending-related compliances cannot be calculated by
the serial rule for spring stiffnesses. By applying again Castigliano’s
displacement theorem it can be shown that the other direct-bending stiffness
is given by the equation:
whereas the cross-bending compliance is:
