How to Measure Elastic Properties with Impulse Excitation

Overview

Impulse Excitation Technique determines elastic properties by measuring a specimen’s resonance frequencies. The calculation depends on the specimen geometry: each shape has its own equations, support positions, and excitation points. This guide covers the three standard geometries defined in ASTM E1876: rectangular bars, solid cylinders, and discs.

Key takeaway: Rectangular bars are the recommended default geometry. They provide all three elastic constants from two measurements and are the simplest to set up.

What You Need

Every IET measurement requires three inputs beyond the resonance frequency itself: the specimen’s dimensions (measured with calipers or a micrometer), its mass (measured on an analytical balance), and the vibration mode being excited. From these, the software calculates the elastic properties using the standardized equations.

The specimen should have smooth, parallel surfaces and uniform cross-section. Surface finish is not critical, but significant chips, taper, or warping will affect accuracy. Measure dimensions at multiple points and use the averages.

Rectangular Bar

The rectangular bar is the most common specimen geometry in IET testing. It is the reference geometry in ASTM E1876 and provides all three elastic properties from two measurements.

Required Dimensions

Measure and record the bar’s length (L), width (w), and thickness (t), along with its mass (m). The length-to-thickness ratio should be at least 5:1, ideally 20:1 or higher, for accurate results.

Flexural Mode → Young’s Modulus (E)

The bar vibrates in a bending motion: the center moves up and down while the nodal points remain stationary. The frequency depends on E, the density, and the bar’s dimensions. Thinner bars vibrate at lower frequencies; stiffer materials vibrate faster.

Torsional Mode → Shear Modulus (G)

The bar twists about its long axis, and opposite corners move in opposite directions. Torsional frequencies are typically higher than flexural frequencies for the same specimen. The width-to-thickness ratio affects how well the torsional mode is excited; bars with a more square cross-section produce clearer torsional signals.

Poisson’s Ratio (ν)

Once you have both E and G, Poisson’s ratio is calculated directly:

ν = (E / 2G) − 1

No separate measurement is needed. Because Poisson’s ratio is derived from the ratio of two independently measured quantities, it serves as an excellent consistency check. An anomalous ν value (outside 0.1–0.5 for most materials) indicates a measurement error in either the flexural or torsional mode.

Solid Cylinder

Cylindrical specimens are common in metallurgy, powder metallurgy, and additive manufacturing. The measurement approach is similar to rectangular bars, with adjustments for the circular cross-section.

Required Dimensions

Measure the cylinder’s length (L) and diameter (d), along with its mass (m). As with bars, a length-to-diameter ratio of at least 5:1 is recommended.

Flexural Mode → Young’s Modulus (E)

Because a cylinder has no preferred bending direction, the flexural frequency is the same regardless of the rotational orientation. This makes the setup less sensitive to positioning than with rectangular bars.

Longitudinal Mode → Young’s Modulus (E) Validation

The longitudinal mode is particularly straightforward for cylinders because the flat end faces make excitation easy. Because it yields E through a different vibration path, comparing it with the flexural result is an excellent consistency check.

Poisson’s Ratio and Shear Modulus

Unlike rectangular bars, cylinders do not have corners that allow clean excitation of a torsional mode. This means G and ν cannot be measured directly from a cylinder specimen. If you need all three elastic constants, use a rectangular bar. For cylinders, Poisson’s ratio can be estimated from published material data or from a companion bar specimen of the same material.

Disc

Disc-shaped specimens are common in ceramics, brake pad materials, and coating studies. The disc geometry uses a different vibration analysis: plate vibration theory rather than beam theory.

Required Dimensions

Measure the disc’s diameter (D) and thickness (t), along with its mass (m). The diameter-to-thickness ratio should be at least 5:1.

Flexural Mode → Young’s Modulus (E)

An important subtlety with disc geometry: the E calculation depends on Poisson’s ratio, and Poisson’s ratio depends on E and G. The software resolves this through an iterative procedure: it starts with an assumed ν, calculates E, then refines ν from the measured modes and repeats until the values converge.

Torsional (Saddle) Mode → Poisson’s Ratio

For discs, Poisson’s ratio is determined from the frequency ratio of the two modes rather than from independently measured E and G. This makes disc measurements slightly less intuitive but equally accurate when the geometry requirements are met.

Practical Tips

Start with rectangular bars if you are choosing specimen geometry. They offer the clearest separation between flexural and torsional modes, the easiest support setup, and the most straightforward measurement procedure. Cylinders and discs are used when the material or application demands that shape.

Verify with Poisson’s ratio. For any geometry, check that the calculated ν falls within the expected range for the material class (0.15–0.30 for ceramics, 0.25–0.35 for metals, 0.30–0.45 for polymers). An out-of-range value almost always indicates a measurement issue: wrong mode identified, poor support positioning, or dimensional error.

Multiple measurements converge. Take at least three measurements for each mode and verify that the frequencies agree within 0.1%. If they do not, recheck the support positions and tap technique. IET is repeatable; scatter indicates setup problems, not method limitations.

Temperature matters. Elastic moduli are temperature-dependent. For precise work, record the specimen temperature or allow it to equilibrate to room temperature before testing. For systematic high-temperature studies, see the IET fundamentals guide for details on furnace-based setups.

Standards Reference

The equations and procedures for all three geometries are defined in these standards: