Nonlinear Sensitivity Analysis of Twin Non-Symmetric Micro-Cantilever Beams

In this paper, the dynamic performance of two parallel micro-cantilever beams is investigated and the results are presented. The dynamic response is of high interest in MEMS structures as it is related to the performance of the micro-devices. The micro-cantilever beams can be easily fabricated and yield high sensitivity to variations of physical quantities. In this work, the dynamic response of two parallel flexible cantilever beams subjected to a difference of potential is analyzed. This configuration was modeled as mass-damper spring systems with two degrees of freedom. Such a system can be used to measure the viscosity of liquids. This viscosity is related to damping between two masses representing the two beams in the discrete system model. The fabrication of two identical beams using MEMS fabrication processes may be difficult as the fabrication process may yield some variabilities. Thus, the two beams may be slightly different which will be reflected in their mass and stiffness. This condition was assumed in the proposed model. As the system is sensitive to the applied difference of potential such that the pull-in voltage represents a good indicator of the sensitivity performance. The dynamic analysis was carried out at potentials close to the pull-in value. Stability of the system was evaluated and the responses of the beams were calculated at a potential close to the pull-in voltage. The sensitivity of the system was calculated for different viscosities of liquid between two beams. It was found that an increase of the viscosity yields higher nonlinearity and consequently loose of accuracy while assuming linear stiffness for the beams. In this research, the stiffness of micro-cantilever beams was calculated from small deflection theory of beams. However, there are other methods that could be considered to evaluate the stiffness of the beams. One of this different methods was considered and the sensitivity of the modeled stiffness is discussed. Since the stiff nonlinear differential equations cannot be solved analytically, the numerical approach was exploited. In this work ISODE method from Maple software was used to solve the model described by the two differential equations.