Relaxation and dynamics of high-stress pre-displaced string resonators

TL;DR

This paper develops an analytical and semi-analytical model for high-stress pre-displaced micromechanical resonators, revealing their static and dynamic behaviors, and validates findings with finite-element simulations.

Contribution

It introduces a new analytical framework for understanding pre-displaced resonators, combining energy-based modeling with finite-element validation.

Findings

Pre-displacement affects stress and frequency in resonators.

Mode shapes and stress distribution are characterized.

Finite-element simulations confirm analytical predictions.

Abstract

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.