Improved Calculation of the Shear Modulus of Rectangular Prisms from Their Resonant Frequency Overtones

Abstract

Abstract The shear modulus (G) is an important parameter for characterizing the strength of and wave propagation through a given material. This study improves the empirical model for estimating shear modulus using the impulse excitation technique based on an experimental analysis of 19 soda-lime silica glass bars. Analysis of the frequency equations relating the shear modulus to the torsional resonant frequencies of rectangular prisms has been used to provide improved equations for calculating G for higher orders of vibration. These were tested by measuring the shear modulus of several novaculite rocks of different porosities up to the seventh order of vibration. These were found to be nearly frequency independent. The updated frequency equations provide a distinct improvement over previously available methods when values for higher order vibrations, and thus the frequency dependence of G, are of interest.