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

Abstract

A novel procedure based on Sturm’s theorem for real‑valued polynomials is developed to predict and identify when periodic or non‑periodic solutions occur in a graphene‑based lumped‑parameter MEMS model, under arbitrary initial conditions. The analytic derivation provides necessary and sufficient conditions on initial data and system parameters, and is validated numerically through Python scripts. Simulations confirm the analytically predicted existence (or absence) of periodic solutions depending on parameter regimes.