Support-Q Optimisation of a Trapped Mode Beam Resonator
Introducing a disorder into a finite periodic oscillatory system induces the presence of a 'trapped mode': a mode in which the displacement field is localised to the region of the disorder. A main inhibitor to MEMS resonators achieving a high quality (Q) factor is energy radiation through the support to the substrate. The trapped modes present a way to tune this to a minimal value. An initial geometry is proposed and contrasted to a lumped-parameter model. Separate two-dimensional resonator and substrate models are used in combination to determine an optimal geometry for maximum support-Q. The support-Q is shown to be on the order of the highest currently available in the literature and the theoretical maximum achievable Q factor is discussed.