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

Daniyar Omarov,Dongming Wei,Piotr Skrzypacz,Daulet Nurakhmetov

doi:10.24132/acm.2018.413

Daniyar Omarov, Dongming Wei + Show 2 more

Open Access

https://doi.org/10.24132/acm.2018.413

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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.

Highlights

An important phenomenon in Micro-Electro-Mechanical Systems (MEMS) is the so called pullin instability
When the voltage is increased beyond a critical value, the device is in the touch-down regime, i.e., the moving part collapses onto the fixed part
The preliminary results for the static pull-in voltage have been stated in [12] by considering the quadratic stress-strain equation which is validated to be important for graphene with applications in MEMS

Summary

Introduction

An important phenomenon in Micro-Electro-Mechanical Systems (MEMS) is the so called pullin instability. For certain values of the voltage the system is in a stable operation regime in which a moving part, e.g., a charged plate, approaches a stable steady state, the so called static pull-in, and remains separate from the fixed part, e.g., a substrate. The preliminary results for the static pull-in voltage have been stated in [12] by considering the quadratic stress-strain equation which is validated to be important for graphene with applications in MEMS. The purpose of this work is to derive the conditions for the dynamic pull-in in the case of general initial conditions in the one degree of freedom (DOF) spring-mass system which. Our mass-spring model can be considered as one DOF approximations to solutions of MEMS problems which usually require applications of advanced finite element solvers, cf [3, 4].

The model problem

Zero initial conditions

Non-zero initial conditions

Conclusions