Air viscous damping effects in vibrating microbeams

P. M. Nieva; N. E. McGruer; G. G. Adams

doi:10.1117/12.658829

17 March 2006 Air viscous damping effects in vibrating microbeams

P. M. Nieva, N. E. McGruer, G. G. Adams

Proceedings Volume 6169, Smart Structures and Materials 2006: Damping and Isolation; 61690N (2006) https://doi.org/10.1117/12.658829
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2006, San Diego, California, United States

Abstract

In this paper, the effect of air viscous damping in the out-of-plane motion of vibrating microbeams is modeled analytically and compared with experimental results. This analysis results in a closed-form expression that can be used to accurately predict the dynamic response of microbeams used in MEMS devices such as vibration and pressure sensors, microswitches, and micromechanical resonators. First, the squeeze-film damping for a solid and straight vibrating cantilever beam, caused by the force in the narrow gap, is analyzed using the well-known Reynolds' equation under the conditions of small amplitude oscillations in an incompressible isothermal squeeze-film. The expression is then modified to include the effects of the initial curled-shape of the microbeams due to fabrication and inherent film stress gradients. Next, the airflow damping, caused by the air surrounding the cantilever beam, is determined by solving the modified form of the Navier-Stokes equation using the bead model, which is based on the oscillation of a string of spheres (beads). The closed-form solution is compared against experimental data gathered during the dynamic characterization of micro cantilever beams with different widths and air gaps. By comparing the measured results to those generated by analytical models, we demonstrate that the damping coefficient match to within 10%.

Citation Download Citation

P. M. Nieva, N. E. McGruer, and G. G. Adams "Air viscous damping effects in vibrating microbeams", Proc. SPIE 6169, Smart Structures and Materials 2006: Damping and Isolation, 61690N (17 March 2006); https://doi.org/10.1117/12.658829

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