Radiation impedance of resonant ultrasound spectroscopy modes in fused silica

The pressure dependence of the resonance frequency of several resonant ultrasound spectroscopy modes in a sample of fused silica has been measured at UCLA in atmospheres of air, helium, and argon near ambient temperature. For both compressional and torsional modes, the radiation resistance is linearly dependent upon pressure and increases with the molecular mass of the surrounding gas. The effects are larger for breathing modes than for torsional modes. They also increase with the molecular mass of the gas. A radiation impedance model is presented which explains some of these data qualitatively and quantitatively. Using the resonant ultrasound spectroscopy (RUS) technique, an attempt was made to determine the third-order elastic constant of solids. This was accomplished by measuring the pressure dependence of the resonance peaks of appropriately shaped samples. Isotropic pressure was exerted by a surrounding gas of helium, air, or argon. Different gases were used in order to experimentally determine the effect of the molecular mass of the gas on the resonance peaks, exclusive of the intrinsic effect of the pressure on the resonance peaks via the third-order elastic constants. Based on the experimental data, a theoretical model was developed to account for the effect of radiation impedance on the resonance frequency of the sample.