Finite Element-based Nonlinear Dynamic Optimization of Nanomechanical Resonators

TL;DR

This paper presents a novel FE-based nonlinear reduced order model combined with derivative-free optimization to efficiently design nanomechanical resonators with multiple conflicting objectives, validated through numerical and experimental results.

Contribution

It introduces an integrated methodology for optimizing nonlinear nanomechanical resonators using FE-based ROMs and multi-objective optimization, improving design efficiency and performance.

Findings

Successfully optimized nanomechanical resonators for Q-factor and Duffing constant.

Validated optimization results through numerical simulations and experiments.

Demonstrated multi-objective optimization for sensing applications.

Abstract

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si3N4 string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano)mechanical resonators with optimized performance for a wide variety of applications.