Elastic Constant Measurement from Vibrational Mode Frequencies in\n Resonant Ultrasound Spectroscopy

Execution of Resonant Ultrasound Spectroscopy (RUS) for accurate measurement\nof elastic constants lies primarily on a perfect matching in the calculated and\nmeasured mode frequencies of free vibration. Calculation of these frequencies\nrequire estimated values of the elastic constants of the material under study,\nand one has to depend on other experiments for these data. The present work\nproposes and demonstrates an alternative to derive initial guess values of\nessential parameters for an isotropic and homogeneous material from the\nacquired RUS spectra itself. Specimen samples are taken in the shape of\nrectangular parallelepiped having nearly same cross-sectional dimension but\nwith different lengths. For particular compressional (shear) mode corresponding\nto length l, the frequency fis inversely proportional to l. The slope m of f\nversus 1/l plot equals to half of the compressional (shear) velocity and this\nin turn gives an estimate of c_11 (c_44). With these parameters as the input\nguess parameters, RUS fitting method is executed to find out the best fit\nresults. Elastic constants of commercially available specimens of aluminium,\ncopper, lead, steel and brass are measured in this technique assuming\nmacroscopic homogeneity. Results show good agreement with available literature\nvalues.\n