Analytical study of coupling element effect on anchor-limited quality factor in double beam array based sensing devices

Energy dissipation through anchor points into the substrate is a major loss mechanism in micro- and nano-mechanical resonators. This work explores the effects of coupling element on anchor loss in double beam array. Finite element analysis is used to evaluate anchor-limited quality factors by computing the ratio of the strain energy stored in the array relative to the energy dissipated into the substrate. Four types of double beam arrays attached to the substrate are discussed. Type 1 and type 2, consisting of coupling elements and two identical primary beams with a frequency ratio of 1:1, are designed for sensing applications. It is noted that the quality factor of in-phase vibration mode changes slightly as the coupling element moving close to the substrate, then jumps up as the coupling element completely attached to the substrate. Contrary to type 1 and type 2, type 3 and type 4, consisting of coupling elements and two non-identical primary beams with a frequency ratio of 1:3, are designed for synchronized oscillation-based applications. A similar jump-up of the quality factor is observed again in both first and second vibration modes. This kind of jump-up is applicable to optimizing the structural design of double beam array especially synchronized one, in order to achieve a high quality factor.