Nonlinear damping in doubly clamped beam resonators due to the attachment loss induced by the geometric nonlinearity

• We show that geometric nonlinearity induces acoustic energy loss at the support.
• The acoustic energy loss results in nonlinear damping of the beam vibration.
• The amplitude dependent quality factor is derived analytically.
• We also derive the nonlinear damping parameter in a reduced order model.

A nonlinear damping mechanism relevant for doubly clamped beam resonators vibrating transversally is proposed and investigated theoretically. The energy loss is a consequence of the axial stress induced along the beam due to the geometric nonlinearity. As the beam vibrates a time varying normal stress is induced at the attachment point which results in acoustic energy loss. Analytical expressions for the resulting amplitude dependent quality factor and the nonlinear damping parameter in a reduced order model are derived considering supports modeled as semi-spaces and as semi-infinite thin plates. The results are expected to be particularly relevant in the analysis of the nonlinear dynamics of suspended beam micro- and nanoresonators, but are not restricted to these particular devices, being valid for similar macroscopic systems.