Effects of disorder in one- and two-dimensional micromechanical resonator arrays for filtering

The effects of disorder on the vibration behavior of arrays of micromechanical resonators are investigated, and the consequences for the characteristics of filters comprised of such arrays are described. Existing understanding of the phenomenon of localization is applied to demonstrate that such devices are particularly sensitive to small variations among resonators which are nominally identical, and that, in the case of high-Q resonators, disorder-induced vibration localization can be a significant impediment to improving filter performance. Numerical simulations are employed to demonstrate the typical effects of different levels of disorder. A novel two-dimensional array of resonators is proposed that is less sensitive to disorder than conventional one-dimensional arrays, improving filter performance without the need for improved manufacturing tolerances.