次谐波对混合层中拟序涡合并过程影响的数值研究

本文用拟谱方法对混合层二涡、三涡的合并规律进行了数值研究,分析了基波和交谐波之间相位差对涡合并过程的影响,并对此进行了解释。计算结果表明：二涡合并有配地和撕裂两种形式,且涡的完全通过撕裂合并的现象仅在相位差为π/2时出现;三涡合并有三种形式。通过计算可见,通过施加多级次谐波并改变它们之间的相位差可以主动控制拟序涡的发展和演变。     

On a bi-stability regime and the existence of odd subharmonics in a Comb-drive MEMS model with cubic stiffness

In this paper we study two different problems. First we present a novel result about the existence of a family of odd subharmonics with prescribed nodal properties for a general nonlinear oscillator with bounded domain and symmetries. Then we apply the general existence result to the Comb-drive finger MEMS model with a cubic nonlinear stiffness term, and prove analytically that the odd positive subharmonic of order two is linearly stable whenever the AC load of the input voltage is small enough. Moreover, we demonstrate a bi-stability regime for this model because the trivial solution $x\equiv 0$ is also linearly stable. The general existence result was obtained through a generalization of the Ortega’s variational principle (Ortega, 2016), and the stability assertions were obtained by following the perturbation approach in Cen et al. (2020) for the linear stability of a nontrivial periodic solution that emanates from the autonomous problem, and the well-known Zukovskii criterion.