Authors: G. Xu, C. Zhang and Q. Jiang
Affilation: University of California, United States
Pages: 579 - 582
Keywords: air-damping, beam, resonator, resonant frequency, electromotive force
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.