Resonant ultrasound spectroscopy of cylinders over the full range of Poisson's ratio

Mode structure maps for freely vibrating cylinders over a range of Poisson's ratio, nu, are desirable for the design and interpretation of experiments using resonant ultrasound spectroscopy (RUS). The full range of isotropic nu (-1 to +0.5) is analyzed here using a finite element method to accommodate materials with a negative Poisson's ratio. The fundamental torsional mode has the lowest frequency provided nu is between about -0.24 and +0.5. For any nu, the torsional mode can be identified utilizing the polarization sensitivity of the shear transducers. RUS experimental results for materials with Poisson's ratio +0.3, +0.16, and -0.3 and a previous numerical study for nu = 0.33 are compared with the present analysis. Interpretation of results is easiest if the length/diameter ratio of the cylinder is close to 1. Slight material anisotropy leads to splitting of the higher modes but not of the fundamental torsion mode. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3559305]