Buzz-o-sonic utilizes the impulse excitation technique1 and complies with ASTM standards E1876 and C1259. These standards describe the impulse excitation techniques as it applies to simple shapes: bars, cylinders, and discs. Please refer to the references for more information. We also provide methods for measuring other shapes such as annular discs (e.g. grinding wheels), tubes, and square plates. Contact us for more details.

The impulse excitation technique, as implemented by Buzz-o-sonic, has been shown to be very precise and reproducible by E. Lara-Curzio, M. Radovic, and L. Riester at Oak Ridge High Temperature Materials Laboratory. On comparing the impulse excitation technique (IE) to some other techniques, it was found that IE gave superior precision and repeatability to nanoindentation and four-point bending. The results were published in Materials Science and Engineering, A368 56-70 (2004).

Put simply, the impulse excitation technique can be described as follows:

An elastic solid is tapped lightly with a small impulse tool (hammer - figure 1) causing the solid to vibrate at its natural frequencies. Although an elastic solid can vibrate in several modes simultaneously (flexural, torsional, and longitudinal), the sample is supported and struck in such a way, that only one mode of vibration is prevalent. The elastic constants can then be calculated from the dimensions and mass of the sample and from the known mode of vibration and the frequency of this vibration. Click here to see QuickTime® movies of Buzz-o-sonic and the impulse excitation technique (broadband connection recommended).

Buzz-o-sonic has built-in algorithms based on the ASTM standards, to calculate the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of bars, cylinders, and discs. A Microsoft® Excel® Spreadsheet is also available. Contact us for more details.

Figure 1: Impulse tool made from a 3-4mm ball bearing cemented to a flexible plastic strip.

Taking the case of bars and cylinders, the flexural mode of vibration is excited by supporting the sample on two knife-edges (typically a polymer foam) placed at 0.224 of the length of the specimen from each end, as indicated in figure 2.

Figure 2: Setup for the flexural mode of vibration for a bar (or cylinder). Out of pane flexure simply means that the bar vibrates up and down, out of the major plane of the bar. One can also strike the bar from the side between the two knife-edges to obtain "in-plane" flexure. It is recommended that the length-to-minimum cross-sectional dimension ratio is 5-25, though much smaller ratios can be measured.

In this example, the rectangular bar is struck lightly in the center with a small impulse tool and the resulting sound is picked up by a microphone placed at one end of the specimen. Note that the microphone and point of impact are both located at the antinodes of the standing wave. Consequently, the position of the microphone and point of impact can be switched. In practice, one tries the various locations for the microphone and points of impact until one obtains the cleanest spectrum (fewest peaks) displayed by Buzz-o-sonic. An example of a clean spectrum obtained on a ceramic is shown in figure 3.

Figure 3: Clean spectrum obtained on a ceramic sample for the flexural mode of vibration

The flexural resonant frequency is 3221 Hz, as shown in the spectrum (upper graph). Note that the waveform (lower graph) has a smooth exponential decay envelope, also indicative of a clean spectrum.

Now, the Young's modulus can be calculated from the flexural resonant frequency and specimen dimensions and mass for a known or assumed Poisson's ratio. One can also measure the shear modulus by obtaining torsional resonant frequency measurements. The setup for this is shown in figure 4.

Figure 4: Setup for the torsional mode of vibration for a bar (or cylinder). Note that the knife-edges are in a cross configuration. For minimizing experimental difficulties, the width-to-thickness ratio should be at least five. Ideally, the length-to-thickness ratio should be 5-25. Note that the microphone and points of impact are on the locations for the nodes under the flexural mode of vibrations. This reduces or eliminates unwanted flexural peaks in the spectrum.

If one measures both the flexural and torsional resonant frequencies, then the Poisson's ratio can also be calculated.

The longitudinal resonant frequency may be measured instead of the flexural resonant frequency to obtain the Young's modulus. The setup is shown in figure 5.

Figure 5: Setup for longitudinal mode of vibration for a bar (or cylinder). The sample is supported across the mid-length. Ideally, for a square cross-section, the length/width ratio should be at least 1.15. For a rectangular cross-section, the length/cross section diagonal should be at least 0.82. For a cylinder, the diameter should be at least equal to the length.

For the case of circular plates or discs, a slightly different method is used to determine the elastic constants. This is because the shear modulus cannot be measured directly as the torsion mode of vibration cannot be excited. For discs then, the shear modulus is not measured directly but is derived from the measured Young’s modulus, and from the Poisson’s ratio which can be measured directly from the ratios of the resonant frequencies for other modes of vibrations (flexure and antiflexure), as shown in figure 6.

Figure 6: Setup for a) antiflexural, and b) flexural mode of mode of vibration for a disc. Ideally, the diameter-to-thickness ratio should be at least four and 10-20 for experimental simplicity. Note that both flexure and antiflexure can be measured on the same set of fixtures, as shown in c).

1Also known as the impulse excitation of vibration, resonant vibration, impact acoustic resonance, ping test, and eigen frequency methods.

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