Analysis of Dynamic Pull-in for a Graphene-based MEMS Model

Abstract

A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic solutions and non-periodic solutions in the pull-in analysis of 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 is no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the periodic solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions. Also, Low Order Fourier Approximation is used to find the solution for the linear spring case. Comparison with the highly accurate Runge-Kutta method is done to verify derived values from the new numerical approximation.