The static and dynamic behavior of a simple parallel-plate capacitor with Casimir force

The static and dynamic behavior of a fixed-fixed beam under the effect of Casimir force is studied. Two different corrections are studied: the effect of real conductor (in contrast to the ideal conductor) on the Casimir force, and the effect of electrode roughness on the electric and Casimir forces. The bifurcation di-agrams and the phase portraits are presented and compared. The chaotic behavior of the system is stud-ied for the case a harmonic voltage is added to the dc voltage, and there is a damping force. It is shown that for autonomous systems (no ac voltage and no damping), the stable region is enlarged when real conductor corrections are applied, applying both the real conductor and roughness corrections shrinks the stable region (compared to applying only the real conductor corrections). Finally, the appearance of chaotic behavior is investigated and the threshold values of the control parameters are found, in the per-turbative limit (small values of the harmonic and damping forces). The chaotic regions are compared for the flat ideal, flat real, and rough real cases. (c) 2021 Elsevier Ltd. All rights reserved.