Dynamic instability analysis of U-shaped electromechanical nano-sensor operated in vdW regime

U-shape nanoelectromechanical systems (NEMS) are potential for developing miniature sensors. While the electro-mechanical performance of conventional beam-type NEMS has been exclusively addressed in the literature, few works have considered this phenomenon in U-shaped systems. Herein, the static and dynamic pull-in instability of the U-shaped NEMS is investigated under the presence of vdW force. Based on the recently developed consistent couple stress theory (CCST), the size-dependent constitutive equation is derived. Two types of the beam cross-sections including rectangular and circular geometries are considered. The nonlinear equations are solved by employing Ray-leigh-Ritz solution method. The developed model is validated by comparison with the results presented in literature. The effect of various parameters on the static and dynamic pull-in parameters, phase plans and stability threshold of the system is discussed. The obtained results reveal that the vdW attraction decreases the pull-in voltage while the size dependency enhances the instability voltage. On the other hand, the presented model demonstrates that characteristics of the tip-plate can change the pull-in parameters significantly