Dynamic stability of electrostatic torsional actuators with van der Waals effect

• Published in: International journal of solids and structures Vol. 43; no. 3; pp. 675 - 685
• Main Authors: Guo, Jian-Gang, Zhao, Ya-Pu
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2006
• Subjects: Bifurcation; Electrostatic torsional actuator; Heteroclinic orbit; Homoclinic orbit; Periodic orbit; Pull-in; Stability; van der Waals force; Pull-in; van der Waals force; Heteroclinic orbit; Stability; Homoclinic orbit; Bifurcation; Periodic orbit; Electrostatic torsional actuator
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2005.03.073

The influence of van der Waals (vdW) force on the stability of electrostatic torsional nano-electro-mechanical systems (NEMS) actuators is analyzed in the paper. The dependence of the critical tilting angle and voltage is investigated on the sizes of structure with the consideration of vdW effects. The pull-in phenomenon without the electrostatic torque is studied, and a critical pull-in gap is derived. A dimensionless equation of motion is presented, and the qualitative analysis of it shows that the equilibrium points of the corresponding autonomous system include center points, stable focus points, and unstable saddle points. The Hopf bifurcation points and fork bifurcation points also exist in the system. The phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, as well as homoclinic orbits.