Li Zhang

The dynamic pull-in instability of a microstructure is a vast research field and its analysis is of great significance for ensuring the effective operation and reliability of micro-electromechanical systems (MEMS). A fractal modification for the traditional MEMS system is suggested to be closer to the real state as a practical application in the air with impurities or humidity. In this paper, we establish a fractal model for a class of electrostatically driven microstructure resonant sensors and find the phenomenon of pull-in instability caused by DC bias voltage and AC excitation voltage. The variational iteration method has been extended to obtain approximate analytical solutions and the pull-in threshold value for the fractal MEMS system. The result obtained from this method shows good agreement with the numerical solution. The simple and efficient operability is demonstrated through theoretical analysis and results comparisons.

A fractal model for pressure drop through a cigarette filter is suggested, the fractal dimensions of both a single fiber and the filter?s cross-sections are calculated, which are two main factors affecting the pressure drop. The two-scale transform is made to convert the fractal derivative model on a smaller scale to an approximate continuous model on a larger scale, so that the model can be easily solved. An optimal filter structure is suggested for minimal pressure drop.