Mechanical resonance of quartz microfibers and boundary condition effects

Abstract

We have measured the mechanical resonance of microscale quartz fibers to qualify the method of obtaining the Young's modulus of nanowires from their resonance frequency and geometry. An equation for a circular beam with a linearly varying cross-section is derived and used to calculate the resonance frequency shift. We have established a model to discuss the boundary condition effect on the resonance frequency. The Young's modulus of the quartz fibers has been determined by measuring the resonance frequency, and the geometry, and by applying the model that treats the influence of the type of clamp. The mean value from measurements of the fundamental resonance on 14 different microfibers is 70+/-6 GPa. This mean value is close to 72 GPa, the Young's modulus of bulk fused quartz. Four resonance modes were observed in high vacuum and air. The mechanical resonance in high vacuum is linear at the fundamental vibration mode, and nonlinear for higher modes.