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Principles of Microelectromechanical Systems by Ki Bang Lee

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CHAPTER 3

STATICS

As a branch of mechanics, statics is concerned with force and moment on mechanical structures in static equilibrium. Using statics, we can analyze forces and moments acting on mechanical structures and evaluate stress, defined as force per unit area, displacement, or deformation of a structural element. Structural elements are essential for MEMS since every component of a MEMS device consists of mechanical structures such as plates and flexures. For a desired function, mechanical structures must be stable and move properly.

3.1 STATIC EQUILIBRIUM

Let us consider a system that consists of an object subjected to forces and moments. If the system produces no motion, the system is in static equilibrium. For example, consider a rock that is placed on the ground as shown in Fig. 3.1a. Since the gravitational force is an attractive force, the rock in Fig. 3.1a weighs mg, where m and g denote the mass of the rock and the gravitational acceleration, defined as approximately 9.8 m/s2 on the surface of the Earth. As shown in Fig. 3.1b, the weight mg, also known as the gravitational force, acts on the center of the rock and the ground generates a counterforce to support the rock. The counterforce N must be mg to maintain equilibrium. If a diagram like that of Fig. 3.1b shows all external forces acting on an isolated body, the diagram is called a free-body diagram. Since the force is a vector quantity that is represented by its magnitude and direction, we can use the vector ...

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