Relaxation and dynamics of stressed predisplaced string resonators

Predisplaced micromechanical resonators made from stressed materials give rise to new static and dynamic behavior, such as geometric tuning of stress. Here, an analytical model is presented to describe the mechanics of such predisplaced 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 predisplacement dependence of stress and frequencies is studied semianalytically. The analysis is extended with finite-element simulations, including the mode shapes, the role of overhang, the stress distribution, and the impact of film stress on beam relaxation.