Modal testing and analysis and how to use eigenvalues, eigenvectors and damping factors for model updating

What is modal testing and analysis?

Modal analysis is a process of extracting natural frequencies, damping factors and mode shapes from measured vibration data.

The measured vibration data is obtained by modal testing at different locations on the structure. As relative motion is sought.

Introduction to modal testing

Let's recap:

  • On our vibration page we discussed vibration, vibration measurements, surveys and assessments

  • On our structural dynamics page we discussed how these measurements relate to each other.

  • Modal analysis is discussed on this page as it is the pinnacle of structural analysis under vibration and shock conditions.

Why is modal analysis important?

As mentioned above, it is the extraction of:

  • Natural frequencies or eigenvalues

  • Mode shapes or eigenvectors

  • Damping factors

Thus, providing more dynamic detail of the structure under vibration or shock.

Let's take a look at modal analysis as performed on finite element software.

Finite element software uses singular value decomposition (SVD) to extract the modal parameters. The SVD results are the eigenvectors and their corresponding eigenvalues. Better known as mode shapes and natural frequencies.

But are these results correct?

The results of the SVD are from a model in the finite element software. Several assumptions were made when modelling the object or structure. Several boundary conditions were also applied.

But is the model completely representative of the real thing? Maybe not?

That is why assumptions were made. The software cannot completely model the physical item.

Too many in the engineering world rely solely on Computer Aided Engineering (CAE). And too few measure and analyse what actually occurs on a physical structure. It is only the physical structure that matters!

When products fail on test. Ask what analyses of the model and model updating were performed on the analytical model?

Finite element analysis and numerical model updating

The value of modal analysis is understanding the true behaviour of physical structures. Then using the results to update the model in finite element analysis software or whatever software you are using.

This approach gives you confidence in your model. Now the model mimics the physical item. And you now can believe the results, and modify the design to more favourable behaviour.

Engineering for the environment

Natural frequencies are frequencies at which the structure is at resonance. At resonances the structure goes into a mode shape, which is the highest deflection that a point will have from equilibrium in that frequency vicinity.

High deflections relate to high bending curvature.

Which relates to surface strain. Compressive on the concave side, tension of the convex side of an element.

Tensional strain relates to fatigue, and fatigue relates to product life.

Product life relates to warranty.

Bottom line. Poor warranty hits your bank account. It's a liability.

Avoid resonances at all costs, i.e. you do not want to excite structural resonances unnecessarily.

Modal testing and analysis case study

An electrical distribution unit for a helicopter had one large electrical contactor. The contactor was located in the centre of the fabricated box.

So, during vibration testing 1g sinusoidal sweep, the drive signal excited the first mode shape. This mode shape was a pure heave mode, and excited the contactor vertically.

On the aircraft, the main function of the contactor is to stay close. Closed circuit so that power could go to the aircraft electronics from the generators. And have current flowing through the contacts themselves.

But as this unit had power across the contactor points, and the contactor had to stay closed throughout the test, it did not. It opened during the vibration sweep at the first mode shape.

Unfortunately, the finite element model was not updated using modal analysis data. And it was first seen during testing.

The most unfortunate aspect was the frequency of this first mode shape. It coincided with the main rotor blade pass frequency.

Had the design process included development testing, this wouldn't happen.

And this is why you should incorporate model updating from modal analysis parameters. So that the model is behaving as the real thing.

We have been in this field, going on 25 years. Because we love structural dynamics. The hands-on aspect balanced with the theoretical work.

Contact us if you need modal testing and analysis done on a structure or product. We love this field, and are here to help you improve your products.

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