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

Daniyar Omarov, Daulet Nurakhmetov, Dongming Wei, Piotr Skrzypacz

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

Číslo: 1/2018
Periodikum: Applied and Computational Mechanics
ISBN: 1802-680X
DOI: 10.24132/acm.2018.413

Klíčová slova: MEMS; graphene, pull-in, periodic solutions, singularity, Sturm's theorem, existence of solutions, grafen, periodické řešení, singularita, Sturmova věta, existence řešení

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Anotace: 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.