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On the application of Sturm's theorem to analysis of dynamic pull-in for a graphene-based MEMS model

机译:Sturm定理在基于石墨烯的MEMS模型动态吸合分析中的应用

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A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic and non-periodic solutions for a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there are no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions.
机译:开发了一种基于Sturm定理的实值多项式的新颖程序,以预测和识别具有初始条件的基于石墨烯的MEMS集总参数模型的周期和非周期解。证明了在集总参数和初始条件的特定条件下,模型具有一定的周期解,否则就没有这种解。通过使用Python脚本进行数字实现以验证解决方案的预期行为,可以使此理论过程变得切实可行。用样本数据进行数值模拟,以证明该程序证明了解析预测的周期解的存在。

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