The air-damping effect on the resonant frequency and the quality factor of a micro- and nano-machined beam resonator is studied. The beam, placed in a uniform magnetic field, is driven to vibrate transversely by the Lorentz force generated by an electrical signal passing through a lead attached to the beam. Based on the Oseen solution of the drag force acting on an infinite long cylinder that moves in incompressible viscous fluids at low Reynolds numbers, the air drag to the beam vibration is characterized and incorporated into the linear elastic beam theory. The analytical results show that air-damping generally shifts the resonant frequency downward and degrades the quality-factor, and that this effect increases as the dimension of the beam decreases. In addition, the frequency response of the electromotive force generated by the motion of the resonator in the magnetic field is also obtained, including the influence of high frequency modes. Based on the quantitative numerical results, it is concluded that the air-damping effect can be significant for sub-micron resonators for frequency-agile applications, while the high frequency mode effect appears to be negligible under realistic physical circumstances.
Journal: TechConnect Briefs
Volume: Technical Proceedings of the 2000 International Conference on Modeling and Simulation of Microsystems
Published: March 27, 2000
Pages: 579 - 582
Industry sector: Sensors, MEMS, Electronics
Topicss: Micro & Bio Fluidics, Lab-on-Chip, Modeling & Simulation of Microsystems