Analysis of U-shaped NEMS in the Presence of Electrostatic, Casimir, and Centrifugal Forces Using Consistent Couple Stress Theory

A mathematical model is used to study the effects of the electrostatic, Casimir and centrifugal forces on the static behaviors of the two U-shaped NEMS with rectangular and circular geometries. The size-dependent equations are obtained by employing the consistent couple stress theory (CCST). The D’Alembert principle is used to transform the angular speed into an equivalent static centrifugal force. The equivalent boundary condition technique is applied for obtaining the governing equation of the U-shape actuator. The nonlinear equations are solved by two different approaches, i.e., using a distributed parameter model (in conjunction with Rayleigh–Ritz solution method) and a lumped parameter model. The model is validated by comparing the obtained results with those of experiment as well as finite element simulation. The effect of various parameters on the instability threshold and characteristics of the system is discussed. The obtained results are beneficial for design and fabrication of U-shaped sensors.