Improved calculation of the Young's modulus of rectangular prisms from their resonant frequency overtones by identifying appropriate shear constants

Abstract

Young's modulus is an important parameter for characterizing the strength of, and wave propagation through, a given material. This study improves the estimation of Young's modulus using the impulse excitation (IE) technique based on an experimental analysis of 19 borosilicate glass bars. Analysis of the frequency equations relating Young's modulus to the out of plane and in plane flexural resonant frequencies of rectangular prisms has been conducted for both the fundamental frequency and its overtones at higher orders of vibration. The Young's modulus of three novaculite rocks with various porosities were then measured up to the seventh order of vibration to validate the optimum shear constant equation for estimating Young's modulus. Young's modulus was found to be nearly frequency independent for these rock samples.