Asymptotic Behavior of Resonant Frequencies in Cylindrical Samples for Resonant Ultrasound Spectroscopy

Abstract: Resonant ultrasound spectroscopy (RUS) is a non-destructive technique for assessing the elastic and anelastic properties of materials by analyzing the frequencies of free vibrations in samples with known geometry. This paper explores the asymptotic behavior of eigenfrequencies in samples with cylindrical geometry. Extending prior research on cuboid samples, our study represents another step toward characterizing asymptotic behavior in arbitrarily shaped samples. While our findings are specific to cylindrical geometries, they are particularly relevant since many RUS samples adopt this shape. Furthermore, we present results on computing derivatives of Zernike polynomials, which may enhance the efficiency of resonant frequency calculations in the RUS method.