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

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.

arXiv comment12 pages, 6 figures

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Cited by in corpus (2)

• On Convergence of a Three-Layer Semi-Discrete Scheme for the Nonlinear Dynamic String Equation of Kirchhoff-Type with Time-Dependent Coefficients
• Spatial mapping of intrinsic and readout nonlinearities in a strongly-driven micromechanical membrane