Department of Physics, Alzahra University, Tehran 1993891167, Iran.
Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, 9747 AG Groningen, the Netherlands.
Phys Rev E. 2018 Aug;98(2-1):022210. doi: 10.1103/PhysRevE.98.022210.
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 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 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 likely 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.
我们研究了 Casimir 力和静电力对具有广泛电导率范围（超过三个数量级）的双梁扭转微机电系统的影响。对于无摩擦的自主系统，分岔和相空间分析表明，在双扭转系统两侧施加相等和不相等的电压时，稳定和不稳定的工作模式之间存在显著差异，分别导致异宿和同宿轨道。对于相等的施加电压，只有对称不稳定鞍点平衡位置取决于材料的光学性质和静电效应，而在任何其他情况下，稳定和不稳定的平衡点取决于这两个因素。对于周期性驱动系统，使用 Melnikov 函数方法来证明混沌运动的存在，这使得预测长时间内是否会发生粘连或稳定驱动成为不可能。混沌行为会带来很大的粘连风险，对于经历更强 Casimir 力和扭矩的电导率更高的系统，这种风险更容易发生。事实上，当施加不相等的电压时，对于电导率最高的系统，混沌运动对静电的敏感依赖性更为明显。
