The role of axial pre-tension in reducing energy dissipation of micro/nano-mechanical resonators

Abstract

Pre-tension is usually applied to raise the frequency of resonators. Theoretical studies revealed that tensile stress could inhibit thermoelastic damping of the resonators and thus increase the quality factor when thermoelastic damping is dominant. Up to now, there is little theoretical investigation for its impacts on other energy dissipation mechanisms, especially support loss. In this paper, a concise formula for the support loss of doubly clamped beam resonators with pre-tension is derived. Then theoretical analyses are carried out, revealing that the pre-tension decreases thermoelastic damping but increases support loss of micro-beam resonators. Making a trade-off between two competing influences of the pre-tension on support loss and thermoelastic damping by tuning pre-tension, an optimal quality factor can be achieved when these two dissipation mechanisms are dominant. Theoretical results of effects of pre-tension on thermoelastic damping and support loss are verified by finite element simulation, and the theoretical prediction of the quality factor associated with these two energy dissipation mechanisms also has the similar trend to the experimental data of reported researches. As a result, the quality factor can be improved by tuning the axial pre-tension in the case that thermoelastic damping greatly surpasses support loss of the resonator. Application of axial pre-tension is further demonstrated to be an effective approach to improving the quality factor of most polymer-based beam resonators. Hopefully, this work will provide theoretical basis and practical guidelines to the design and development of high-performance micro/nano resonators.