Page 53 - Mechanics of Microelectromechanical Systems
P. 53
40 Chapter 1
The out-of-the-plane compliances are:
5.3.2 Thin Curved Beams
The in-plane and out-of-the-plane compliances are now derived for a thin
beam (R/w > 10), according to Fig. 1.20. The beam is also considered long,
which enables ignoring the shearing effects.
5.3.2.1 In-Plane Compliances
The two linear displacements about the x- and y-directions, together with
the rotation about the z-axis, are again calculated by means of the generic
formulation of Eqs. (1.125). The strain energy, as mentioned, includes only
the bending moment, and therefore is of the form:
