# High Definition Modal Testing

### Is it all it’s Tapped Up to be?

## The Challenge

Impact testing is one of the oldest and most versatile methods of experimental modal testing around. It’s quick to setup, needs only basic instrumentation and can be done by one person.

So when challenged with even the most complicated structure the experienced modal tester won’t be daunted, the process is always the same. Measure up geometry and assess the response of the structure. From this the tester will investigate some key properties. Is it a linear structure and does it obey Maxwell’s Reciprocal Theorem(1)? Where is a good place to excite the structure, and will it capture all the modes of vibration? What is needed in terms of excitation bandwidth? How much damping is present, how long the response will take to die away? Once all these questions are answered then testing and analysis should give a good insight into the dynamic behaviour of the structure and permit correlation with Finite Element (FE) models.

But it will always be a compromise, trying to balance out the number of points to characterise the structure with the time it takes.

**Tapping all day**

To have a look at this compromise I challenged our laboratory team to measure a crankshaft from a modern four cylinder engine. Being a forged iron part they always give a good response, but the complicated shape makes a crankshaft one of the trickiest automotive parts to test. But undeterred our testing team recovered a very respectable geometry of 70 points, enough to describe the shapes, joints and major features of the crankshaft.

They surveyed and assessed where to place the accelerometer to get a good response measurement, what hammer tips to use to excite the modes of interest and what windowing and frequency range to use. They then set about tapping all of the 70 points in as many directions as were reachable. The full measurement set was then analysed and gave a very respectable line model, more than enough to have a good attempt at a correlation with finite element (FE) correlation on the first bend in a couple of axis. But for any detailed study on the structure you would have to refer back to the FE model to determine what was really going on.

**The Robot Way**

As a communication tool it’s fantastic, no matter the level of your audience everyone can see the shape of the actual structure in your test model, it avoids the debates of which end is which in your test and allows a much more focused discussion on the issue rather than being side tracked by doubts and debate on the nature of the approximate geometry.

(1) Maxwell’s Theorem.

The displacement of a point *B* on a structure due to a unit load acting at point *A* is equal to the displacement of point *A* when the unit load is acting at point *B*, that is, *f _{BA}* =

*f*.

_{AB}The rotation of a point *B* on a structure due to a unit couple moment acting at point *A* is equal to the rotation of point *A* when the unit couple moment is acting at point *B*, that is, α* _{BA}* = α

*.*

_{AB}These are useful for 2nd-degree-indeterminate and higher structures.