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

D. Omarov; D. Nurakhmetov; D. Wei; P. Skrzypacz

doi:10.24132/acm.2018.413

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

D. Omarov, D. Nurakhmetov, D. Wei, P. Skrzypacz

Nazarbayev University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	59-72
Number of pages	14
Journal	Applied and Computational Mechanics
Volume	12
Issue number	1
DOIs	https://doi.org/10.24132/acm.2018.413
Publication status	Published - Jan 1 2018

Keywords

Existence of solutions
Graphene
MEMS
Periodic solutions
Pull-in
Singularity
Sturm’s theorem

ASJC Scopus subject areas

Biophysics
Computational Mechanics
Civil and Structural Engineering
Fluid Flow and Transfer Processes
Computational Mathematics

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title = "On the application of Sturm{\textquoteright}s theorem to analysis of dynamic pull-in for a graphene-based MEMS model",

abstract = "A novel procedure based on the Sturm{\textquoteright}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.",

keywords = "Existence of solutions, Graphene, MEMS, Periodic solutions, Pull-in, Singularity, Sturm{\textquoteright}s theorem",

author = "D. Omarov and D. Nurakhmetov and D. Wei and P. Skrzypacz",

note = "Funding Information: This research was supported by the Nazarbayev University ORAU grant “Modeling and Simulation of Nonlinear Material Structures for Mechanical Pressure Sensing and Actuation Applications”.",

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AU - Skrzypacz, P.

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AB - 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.

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