Using Specimen Geometry to Isolate Flexural and Torsional Vibration Modes During Sonic Resonance

Abstract

Abstract The ASTM E1875 method of sonic resonance is a convenient means of obtaining the elastic material properties of materials, particularly at high temperatures. The technique is performed by exciting a rectangular bar specimen to vibrate over a range of frequencies while measuring the amplitude of the bar’s vibrations. At specific frequencies, a local maximum in the displacement amplitude denotes either flexural or torsional resonance. The elastic and shear moduli are then computed from the first flexural and torsional resonant frequencies, respectively, as well as from the mass and dimensions of the bar. However, for certain bar geometries, the sequence in which the different resonant frequencies occur depends on the Poisson’s ratio of the material. Because the amplitudes measured during the tests do not distinguish between flexure and torsion, and because Poisson’s ratio is generally not known a priori, it is desirable to select specimen geometries for which only one sequence of frequencies is possible. This paper presents an analytical approach to determine what Poisson’s ratio would need to be in order for the first torsional frequency to always be higher than the second flexural frequency. This critical value for Poisson’s ratio is shown to be a function solely of geometry and can therefore be selected at will through the choice of length, width, and height of the bar. When the critical Poisson’s ratio is chosen to be greater than 0.5 and therefore non-physical, the first torsional frequency of the bar will always be higher than the second flexural frequency, regardless of the material composing the bar. A comparable approach is used to identify geometries that ensure that the first torsional frequency is always less than the third flexural frequency. When one selects geometries for which the sequence of the different resonant modes is known, the actual Poisson’s ratio of the material is no longer needed to compute the elastic constants.