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

TL;DR

This paper enhances the accuracy of Young's modulus estimation for rectangular prisms by analyzing resonant overtones and identifying appropriate shear constants, validated through experiments on glass bars and rocks.

Contribution

It introduces an improved method for calculating Young's modulus using resonant overtones and optimal shear constants, validated with experimental data.

Findings

Young's modulus is nearly frequency independent in tested rocks.

Resonant overtones provide reliable data for Young's modulus estimation.

Optimal shear constants improve the calculation accuracy.

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.