Nonlinear support loss in micro/nano beam resonators induced by geometric nonlinearity

Support loss, as one of the main energy dissipation sources in micro/nano mechanical resonators, is generally evaluated by linear theories without considering mid-plane stretching. Predictions of support loss based on linear elastic theory cannot be applied to resonators working in nonlinear regime with large vibration amplitude. In this regard, we investigate the support loss of a doubly clamped micro/nano beam resonator in in-plane flexural vibration in this study, with both geometric nonlinearity and axial pre-tension considered, aiming to accurately model the support loss for high-performance resonators under large-deflection vibration. The expression of support loss is derived, with both the normal stress induced by the mid-plane stretching and shear stress distributed in the attachment region of the support taken into account. The analytical model proposed in this work is validated by finite element simulations and the experimental data of previous studies. Furthermore, the influence of the axial pre-tension on nonlinear vibration properties and that of the vibration amplitude on the support loss are probed. The effects of the axial pre-tension and the aspect ratio on the support loss are also analyzed. The analytical results demonstrate that the mid-plane stretching effect due to geometric nonlinearity leads to larger support loss, and the support loss increases with vibration amplitude. Hopefully, the nonlinear model of support loss developed in this work may provide guidelines to evaluate the support loss and elucidate the phenomenon of the support loss increasing with vibration amplitude.