The effect of capillary and intermolecular forces on instability of the electrostatically actuated microbeam with T-shaped paddle in the presence of fringing field

Abstract

• The mechanical behavior of a clamped–clamped microbeam with middle paddle is analyzed. • The pull in voltage declines and the deflection enlarges as the intermolecular forces increase. • Presence of the electrostatic force accelerated the instability resulting from the capillary force . • Fringing field effect considerably affected determination of the bifurcation points . The present study is aimed to investigate pull-in instability, static deformation, natural frequency, primary and subharmonic resonances in the clamped–clamped microbeam with middle T-shaped paddle in presence of electrostatic force, Casimir force, van der Waals force and fringing field effect; besides, it is focused on investigating the effect of capillary force on instability and adhesion considering the effects of middle layer elongation and axial force. The microbeam is modeled as an Euler Bernoulli beam. In order to solve the nonlinear equations, the Galerkin-based rank reduction method was used. The discretized equations are solved by the perturbation theory in the neighborhood of primary and subharmonic resonances. The obtained results showed that the van der Waals and Casimir forces had attractive nature and led to the increased static deformation as well as occurrence of the pull-in at lower voltages; besides, the effects of attraction in Casimir was more than that in van der Waals. Results showed that with increase in the dimensionless length, which is influenced by the capillary force, the maximum static deformation was increased as well, leading to instability in capillary coefficients. Furthermore, presence of the electrostatic force also accelerated the instability resulting from the capillary force. Effects of the axial force and elongation in the clamped state resulted in the reduced static deformation as well as delayed instability. It is shown that changing the Casimir and Van der Waals forces as well as the fringing field effect, in addition to causing changes in the voltage and range, considerably affected determination of the bifurcation points. To validate the analytical results, numerical simulation is performed.