Impulse Excitation Technique

Start from what a solid is: a lattice of balls (the atoms) joined by springs (the bonds). The three material numbers are three things you can do to it. Young’s modulus E: pull the ends apart, and the springs stretch and push back. Poisson’s ratio ν: as you pull, the sides draw in and the bar gets thinner, and ν is how much (metals sit near 0.3). Shear modulus G: shove the top sideways so it leans, and G is the resistance to that.

Only two of the three are independent, and you can see why. Lean a square and watch its diagonals. Shearing is stretching one while squeezing the other:

So shear is built out of stretch (E) and the sideways coupling (ν), and it reduces to the identity G = E / 2(1+ν). That is why one bending note and one twisting note together pin down ν.

The Impulse Excitation Technique (IET), standardised as ASTM E1876, is that chain run backwards: because stiffness, mass and shape set the frequencies, the measured frequencies give the stiffness back. Rest the part on its still points, tap it, and read the ring. A bending peak gives E, a twisting peak gives G, and ν follows. For a bar, rod or disc the standard’s formulas invert it to about 1%. For any other shape we fit a finite-element model of your real part, validated to ~0.15% against our reference bar. How fast the note fades is damping. In the lab an internal crack raises it, the property we develop for crack detection.