Resonance frequencies of parallelepipeds for determination of elastic moduli: An accurate numerical treatment

The elastic resonance and impulse excitation of vibration are standard techniques to determine the elastic moduli of materials, with important applications to glass, metals, ceramics, rocks, etc. The validity of the analytical expressions used for prismatic bars is analyzed in detail in this work by numerically solving the three-dimensional linear elasticity equations, providing in particular error estimations for the formulae in ASTM standards. The results help to choose the sample dimensions, indicate which expressions are better to use in order to achieve some desired level of accuracy, and provide a means to correct the obtained results.