论文标题
周期性解决方案和避免在非自主微型机械系统中不稳定的拉力 -
Periodic solutions and the avoidance of pull--in instability in non--autonomous micro--electro--mechanical systems
论文作者
论文摘要
我们研究了一级自由微机械系统（MEMS）的定期解决方案，并在$ t $ - 周期性静电强迫下使用平行板电容器。我们获得了有关在任意非线性恢复力以及使用石墨烯固定在弹簧上的弹簧时，有关问题的$ t $周期解决方案的存在分析结果。然后，我们在$ t- $周期性的poincar {é}图上进行数值演示，这些解决方案通常在本地稳定，周围有较大的“岛屿”，其较大的“岛屿”，其中完全避免了吸水稳定性。我们还在Poincar {é}地图上以图形方式证明了具有较高时期$ nt，n> 1 $的稳定的周期性解决方案，对于较大的参数范围，周围有较大的“岛屿”范围，所有初始条件都可以避免所有初始条件避免 - 在不稳定的情况下，从而有助于我们大大增加了这些MEMS模型的安全域。
We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic solutions of the problem in the case of arbitrary nonlinear restoring force, as well as when the moving plate is attached to a spring fabricated using graphene. We then demonstrate numerically on a $T-$ periodic Poincar{é} map of the flow that these solutions are generally locally stable with large "islands" of initial conditions around them, within which the pull-in stability is completely avoided. We also demonstrate graphically on the Poincar{é} map that stable periodic solutions with higher period $nT, n>1$ also exist, for wide parameter ranges, with large "islands" of bounded motion around them, within which all initial conditions avoid the pull--in instability, thus helping us significantly increase the domain of safe operation of these MEMS models.
