Resonant acoustic determination of elastic moduli

Abstract

A long rod of circular or elliptical cross section can be selectively excited in the torsional, longitudinal, and flexural resonant modes using a single pair of electrodynamic transducers consisting of coils glued to each end of the bar and placed in the field of a magnet. The elastic moduli of the material can be simply determined to high accuracy by measuring the resonance frequencies of these modes and the mass and physical dimensions of the rod. Since the longitudinal and flexural modes both yield values for the Young’s modulus, the system has a built-in redundancy that makes the interpretation of the data more robust. The large signal amplitudes make automated measurement of the temperature dependence of the moduli simple through the use of a phase-locked loop to track the change in the resonance frequency with temperature.