Nonlinear acoustic damping mechanism in micro and nanobeam resonators due to nonlinear shear stress at clamping

In this work it is shown how a strong nonlinear increase of the shear stress at the clamping regions of suspended bridge resonators can result in a large nonlinear damping. The multimode Galerkin method is used to demonstrate that the shear stress at the clamping region is enhanced for large amplitudes of vibration as a consequence of the beam deformation induced by the midplane stretching. The extra stress increases the acoustic energy loss through the clampings compared to the one predicted ignoring the effect of the beam stretching on its shape. The total emitted acoustic power is found to be more than two or three times larger for strong nonlinear vibrations. While this new nonlinear damping mechanism is investigated for suspended beam micro and nanoresonators it can have analogs in other physical systems that can suffer nonlinear stretching and generate acoustic waves through the surrounding structures. The damping mechanism evidences the complex interplay between the geometrical nonlinearity and nonlinear damping.