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

Paul A. Bosomworth; Rui Zhang; Lawrence M. Anovitz

doi:10.1520/JTE20230442

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

Paul A. Bosomworth, Rui Zhang, Lawrence M. Anovitz

Geochemistry & Interfacial Science

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	963-976
Number of pages	14
Journal	Journal of Testing and Evaluation
Volume	52
Issue number	2
DOIs	https://doi.org/10.1520/JTE20230442
State	Published - Mar 1 2024

Funding

This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). The authors declare no competing financial interests. ACKNOWLEDGMENTS This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences program.

Funders	Funder number
U.S. Department of Energy
Office of Science
Basic Energy Sciences

Keywords

R factor
impulse excitation
mechanical properties
novaculite
silica glass

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10.1520/JTE20230442

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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.",

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AB - 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.

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

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