CHAPTER 4
STATIC BEHAVIOR OF MICROSTRUCTURES
In Chapter 3 we considered the basic equations for static equilibrium and described approaches to solutions for static behavior. Based on the equations and solutions that were derived, static behaviors of microstructures are described in detail in this chapter. The static behavior of elements of microstructures is dealt with first, then that of microstructures consisting of the elements we described. Afterward, nonlinear behavior of microstructures is covered.
4.1 ELEMENTS OF MICROSTRUCTURES
In the early stage of the development of MEMS, some researchers were interested in rotating machines that were similar to large-scale engines or electric motors. However, they could not develop an efficient rotating machine since the friction between the microstructures plays a critical role. In other words, the input energy is dissipated into heat due to the friction. This phenomenon may be verified by using dimensional analysis, which was covered in Chapter 1; the frictional force is proportional to the contact area between microstructures, and the frictional force in microscale machines becomes dominant. A similar argument holds for the viscous (damping) force due to the viscosity of gas surrounding the microstructures, since the viscous force is also proportional to the area exposed to the surrounding gas. For this reason, most MEMS consist of movable structures whose ends are anchored on a substrate and whose portions are flexible for springlike ...
