标题： 耗散稀释驱动的拓扑优化用于最大化纳米机械谐振器的 $Q$ 因子 显示英文标题

标题： Dissipation Dilution-Driven Topology Optimization for Maximizing the $Q$ Factor of Nanomechanical Resonators

摘要： 纳米机械谐振器的品质因子（即$Q$因子）受几何形状和应力的影响，这一现象被称为损耗稀释。 已有研究探索了最大化这一效应的方法，从而导致了柔性固定谐振器的设计。 本文提出了一种拓扑优化方法，通过最大化损耗稀释来设计具有高$Q$因子的二维纳米机械谐振器。 该方法基于预应力有限元模型的非线性与线性模态刚度比，并结合相应的伴随灵敏度分析公式。 在方形域中的系统化设计产生了与文献中相当的$Q$因子的几何结构。 我们分析了谐振频率和品质因子之间的权衡关系，以及这些关系如何反映在谐振器的几何形状上。 我们进一步将该方法应用于优化六边形全区域内的谐振器。 通过使用整个网格（即，不假设任何对称性），我们发现优化器收敛到一个由四根细长杆组成的两轴对称设计。 显示英文摘要

摘要： The quality factor ($Q$ factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high $Q$ factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable $Q$ factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh -- i.e., without assuming any symmetries -- we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.