Nonlinear Analysis of Pull-in Voltage of Twin Micro-Cantilever Beams with Different Dimensions

Abstract

-Micro-cantilevers are micromechanical structures that are being used in detection and sensing as MEMS. The easy usage and the relatively simple fabrication of micro-cantilever beams make them stand as suitable candidates for a wide variety of engineering applications. Dynamic capability of micro-cantilever beams to withstand considerable impacts and even various static loadings make them useful in applications as AFM, inertial sensors, or flow applications. Specific configurations with micro cantilever beams could be used for more advanced applications such as liquid viscosity measurement. The main objective of this research is to investigate the nonlinear dynamic behaviour of two parallel micro cantilever beams with slightly different geometry under the condition of closed to pull-in voltage. The governing differential equations that model closely the dynamical behaviour microcantilever beams under electrostatic field are used in the formulation. The model is based on discreet 2 degree of freedom mass-springdamping. The electrostatic loading induces the dynamical behaviour of two parallel micro cantilever beams expressed in two differential equations that are nonlinear and stiff. A specific algorithm that optimizes the integration steps which is named ISODE is used to perform the computation. The time response and phase diagram to the step-voltage for the mass-spring-damper system is derived numerically and the pull-in voltage of the system is evaluated.

Viscosity Measurement for Picoliter Liquid Volumes Using Twin Micro-Cantilever Beams

“…The pull-in voltage of the system was numerically calculated from the first order ODE and this way the behaviour of the system close to pull in voltage was studied. Twin micro-cantilever beams with different dimensions was studied in [15]. In this research behaviour of two micro-cantilever beams with different thickness under pull-in voltage was studied.…”

“…The effect of liquid between two beams was studied in [16]. The authors used the same concepts in [15] and studied the behaviour of two micro-cantilever beams under pull-in voltage condition and liquid droplet in between.…”