Micro-cantilever beams are interested structures in MEMS because of their fabrication is very easy and its versatility. The importance of micro-cantilevers beam in MEMS has driven various investigations like static and dynamic performances under different loading such as potential fields. In this research the non-linear differential equation which models dynamics of a micro-cantilever beams vibration subjected to electrostatic field has been studied. The model which has one degree of freedom is used to calculate the pull-in voltage. This model adopted based on different method of calculating stiffness of micro-cantilever beam. The nonlinear ordinary differential equation which used to model the dynamics of the cantilever subjected to electric field close to snap on is highly stiff. Investigation on solving of nonlinear stiff ordinary equation showed that only Lsode algorithm yield to correct solution to the problem. Lsode is equipped with a robust adaptive time step selection mechanism that enables solutions to very stiff problems, as the one under discussion. The best match in the resonant frequency for equivalent stiffness based on four different models was considered. The stiffness model suitable for the best match in deflection is proved to be different from the model that yields. Pull-in voltage under electric field was studied. Pull-in voltage has been investigated from the analytical and numerical perspective. A complete parametric study of structural damping effect on large deflection of micro-cantilever beam was studied was done numerically in this work. Different kind of impulse voltages were considered and effect of them on pulling voltage numerically was studied. A cumbersome mathematical method, Lie symmetry, was used to drive a closed from of time response to step voltage for undamped system and pull in voltage of such system was calculated. Finally, a closed form driven from the nonlinear ODE for calculating pulling voltage was presented.
-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.
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