Effect of van der Waals force on pull-in voltage, frequency tuning and frequency stability of NEMS devices

This paper investigates the influence of van der Waals force on the pull-in instability and free vibration characteristics of electrostatically actuated fixed-fixed beam under axial force. The Euler-Bernoulli beam theory is applied for theoretical formulation. The effects of fringing fields, non-linearity due to mid-plane stretching and van der Waals force are considered. Subsequently, reduced order model based on Galerkin method is used to solve the governing differential equation. The validation for present methodology is established by comparing with previously published experimental and numerical results. After validation of the model, the significance of the van der Waals force on static pull-in parameter and natural frequency is studied in presence of axial force through parametric study. The analysis of obtained results shows that, when high axial compressive force is present in nano-beam, the van der Waals force significantly effects the pull-in parameter, tunability of fundamental natural frequency and resonant frequency stability characteristics of nano devices. It is found that, the frequency can be tuned for some hundred percent in presence of high axial compressive initial stress in nano beam, along with suitable combination of mid-plane stretching and van der Waals force parameters. It is also found that, the design of electrostatically actuated oscillators which exhibit notable frequency stability under variation of temperature is significantly influenced by van der Waals force as it reduces the optimum voltage at which frequency stability occurs. The results are expected to be beneficial for the evaluation of operational parameters of nano devices under the influence of van der Waals force.