Analysis of Dynamic Pull-in Voltage of a Graphene MEMS Model

TL;DR

This paper investigates the dynamic pull-in behavior of a graphene-based MEMS device using bifurcation analysis, deriving conditions for stability and bifurcation points based on nonlinear spring-mass modeling.

Contribution

It provides an analytical and numerical analysis of bifurcation conditions for dynamic pull-in in graphene MEMS, incorporating nonlinear stress-strain relations.

Findings

Derived conditions for the existence of periodic solutions.

Identified bifurcation points related to elastic stiffness and voltage.

Presented numerical illustrations of bifurcation behavior.

Abstract

Bifurcation analysis of dynamic pull-in for a lumped mass model is presented. The restoring force of the spring is derived based on the nonlinear constitutive stress-strain law and the driving force of the mass attached to the spring is based on the electrostatic Coulomb force, respectively. The analysis is performed on the resulting nonlinear spring-mass equation with initial conditions. The necessary and sufficient conditions for the existence of periodic solutions are derived analytically and illustrated numerically. The conditions for bifurcation points on the parameters associated with the second-order elastic stiffness constant and the voltage are determined.