Resonance patterns in cantilevered plates with micro electromechanical systems (MEMS) applications

Detailed maps of the resonance patterns of cantilever plates highlighting width and Poisson's ratio effects are presented. At present, this is lacking in the literature for higher bending and for torsional modes. Ranges of curve crossing and curve veering are identified and their potential effects on micro electro-mechanical systems (MEMS) applications are discussed. Results for three common materials are included. Closed form expressions are presented that could predict three plate resonance types: beam-like, symmetric and anti symmetric (torsional). It is also shown that some torsional vibration formulas used in the literature are inaccurate for wide cantilevers. Although the focus of the discussion is on MEMS, the results are applicable to both macro and micro plates of dimensions greater than 100nm. This is because the analysis was carried out using continuum-based three dimensional finite elements.