Dependence of chaotic behavior on optical properties and electrostatic effects in double beam torsional Casimir actuation

TL;DR

This study explores how Casimir and electrostatic forces influence chaos and stability in double beam torsional MEMS, revealing that higher conductivity enhances chaotic behavior and stiction risk, especially under unequal voltages.

Contribution

It provides a detailed analysis of the dependence of chaotic dynamics on optical and electrostatic properties in torsional MEMS, using bifurcation, phase space, and Melnikov function methods.

Findings

Chaotic motion is more prominent in highly conductive systems.

Unequal voltages increase sensitivity to electrostatic effects.

Chaotic behavior correlates with higher stiction risk.

Abstract

We investigate the influence of Casimir and electrostatic torques on double beam torsional microelectromechanical systems with materials covering a broad range of conductivities of more than three orders of magnitude. For the frictionless autonomous systems, bifurcation and phase space analysis shows that there is a significant difference between stable and unstable operating regimes for equal and unequal applied voltages on both sides of the double torsional system giving rise to heteroclinic and homoclinic orbits, respectively. For equal applied voltages, only the position of a symmetric unstable saddle equilibrium point is dependent on the material optical properties and electrostatic effects, while in any other case there are stable and unstable equilibrium points are dependent on both factors. For the periodically driven system, a Melnikov function approach is used to show the presence of chaotic motion rendering predictions of whether stiction or stable actuation will take place over long times impossible. Chaotic behavior introduces significant risk for stiction, and it is more prominent to occur for the more conductive systems that experience stronger Casimir forces and torques. Indeed, when unequal voltages are applied, the sensitive dependence of chaotic motion on electrostatics is more pronounced for the highest conductivity systems.