Page 16 - Mechanics of Microelectromechanical Systems

1. Stiffness basics 3

Figure 1.2 Rotary/spiral spring: (a) Load; (b) Deformation

Again, Eqs. (1.3) and (1.4) show that the rotary compliance is the inverse of
the rotary stiffness. The rotary spring is the model for torsional bar
deformations and moment-produced bending slopes (rotations) of beams.
Both situations presented here, the linear spring under axial load and the
rotary spring under a torque, define the stiffness as being the inverse to the
corresponding compliance. There is however the case of a beam in bending
where a force that is applied at the free end of a fixed-free beam for instance
produces both a linear deformation (the deflection) and a rotary one (the
slope), as indicated in Fig. 1.3 (a).

Figure 1.3 Load and deformations in a beam under the action of a: (a) force; (b) moment

In this case, the stiffness-based equation is:

The stiffness connects the force to its direct effect, the deflection about the
force’s direction (the subscript l indicates its linear/translatory character).
The other stiffness, which is called cross-stiffness (indicated by the