Impulse Excitation Technique
Measuring Elastic Constants
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.
For testing more complex shapes still, we offer MItools which uses sophisticated mixed numerical-experimental analyses (MNETs). Click here for an example.
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 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 and modes of vibration for a rectangular bar
For the out-of-plane flexure mode of vibration (up and down vibration), 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, the various locations for the microphone and points of impact are tried until the cleanest spectrum (fewest peaks) is obtained and 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.
For the case of circular plates or discs, a slightly different method is used to determine the elastic constants: 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 4.
Figure 4: 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).
Supports can be dispensed with in some cases if damping is not being measured. In these cases the sample is simply laid down on a pad of soft polyurethane foam. The change in frequency due to increased external damping is usually negligible and can be tested for. Below is an example of a disc being tested in such a manner.
Testing a small ceramic disc
Internal Friction (Q-1)
Derived from the waveform [Q-1(w)]
The peak amplitude of vibrations of an impulse-excited solid follows an exponential decay given by:
- Where:
- A = amplitude at time t
- A0 = initial amplitude following impulse excitation
- fn = resonant frequency of interest
= damping ratio which determines system damping capacity
- Where:
= logarithmic decrement = 
- A1 = amplitude at time t1
- A2 = amplitude at time t2
The internal friction is then given by:
Derived from the power spectrum peak bandwidth[Q-1(p)]
The internal friction is also a measure of the breadth of the resonance peak, given by:
It is important that when measuring internal friction that the sample be carefully supported at the nodes for the mode of vibration being used. The supports should also be as thin as possible to reduce external damping. Trial and error may be necessary to determine the best method for supporting a given sample. We find that measuring the internal friction from the longitudinal mode of vibration gives the most consistent results, because the sample can be balanced/clamped and supported on one knife edge, rather than the two knife edges required for flexural measurements. Where possible, we use thin fishing nylon to support the samples.
1Also known as the impulse excitation of vibration, resonant vibration, impact acoustic resonance, ping test, and eigen frequency methods.