Investigation on Pull-in Voltage, Frequency Tuning and Frequency Stability of MEMS Devices Incorporating Casimir Force with Correction for Finite Conductivity

Abstract

This paper studies the influence of Casimir force on the static and dynamic characteristics of electrostatically actuated fixed–fixed microbeam. The theoretical formulation for the study is obtained using the Euler–Bernoulli beam theory. The formulation of governing equation includes the influence of mid-plane stretching of microbeam, fringing field and Casimir force incorporating correction for finite conductivity. The governing differential equation is solved using the Galerkin discretisation method and reduced order model technique. The results of the methodology implemented in current work are validated through comparison with reported numerical and experimental results. Subsequently, the effect of the Casimir force incorporating correction for the finite conductivity on the pull-in voltage and natural frequency is investigated in the presence of the residual stresses in a microbeam. The investigation shows that neglect of the Casimir force significantly overestimates the pull-in voltage; however, inclusion of corrections for the finite conductivity to the Casimir force indicates reduction in amount of overestimation in the pull-in voltage. The linear free vibration characteristics depict that microbeam with high mid-plane stretching parameter in the presence of the compressive residual stress offers tuning of natural frequency for more than two times. Further, the microbeam with high mid-plane stretching parameters provides resonant frequency stability characteristics at high voltage parameters though there is variation in the residual stress due to temperature variation during application. The present work also shows that these frequency tunability and stability characteristics are significantly influenced by the Casimir force. The results of the current work are expected to be valuable for the design of microbeam devices.