  Pre-displaced micromechanical resonators made from high-stress material give
rise to new rich static and dynamic behavior. Here, an analytical model is
presented to describe the mechanics of such pre-displaced resonators. The
bending and tension energies are derived and a modified Euler-Bernoulli
equation is obtained by applying the least action principle. By projecting the
model onto a cosine shape, the energy landscape is visualized, and the
pre-displacement dependence of stress and frequency is studied
semi-analytically. The analysis is extended with finite-element simulations,
including the mode shape, the role of overhang, and the stress distribution.
