MODAL ANALYSIS: A PRACTICAL APPROACH (PART 1)

My name is Leonardo Rosa and I'm a Brazilian Engineer. I live in France for a bit more than 5 years now. Mainly, I work with Structural Calculations for the Aerospace Industry.

Static Analyses are no mystery for Structural Engineers. However, some may face difficulties in the transition to the world of Structural Dynamics. So, I decided to make a series of short Articles, giving some hints about the subject.

I will do my best to use an easy language and provide real world examples. During the process, I'll show a couple of equations to help understanding what the Solver calculates.

As the aim is to reinforce the fundamentals, before any Simulation, I strongly recommend consulting a good Reference Book.

I'll start with Modal Analysis. If I did a mistake, if you like the Article or if you have any suggestion, please, leave a comment so that I can improve in the next ones.

KICK-OFF

A wise Professor of mine used to say something I've never forgotten:

So, that's what we're going to do! We'll check how Modal Tests are done and have a grasp of our final objective. But, before, let's watch some didactic videos.

The first one will introduce the concept of Natural Frequencies and Mode Shapes.

In the Experiment, an eccentric rotating mass was used to create a Steady State Load.

By varying the rotation speed of the engine, the Frequency of the Load changes. As consequence, the Frequency of the plate's Structural Response changes.

Introducing a very important concept: in Linear Dynamics, the Frequency of the Response and Excitation are equal. Therefore, to visualize a Mode Shape, the Frequency of the Engine has to match the Frequency of a Natural Mode.

Now, let's see a different Experiment, that uses the same principle.

From Linear Acoustics, the Frequency of the Source, Reflected and Transmitted Waves must be equal. Off course: in the real world, things are a bit different. But, still, we can say the vibration Frequency of the glass is, approximately, the same as the Acoustic Source's Frequency.

Be careful: the principle is not valid for Amplitude and Power. In other words: the Acoustic Source must have enough Power to increase the Amplitude of the glass Response.

Back to the video: first, someone changes the frequency of the Acoustic Source - which is a Steady State Acoustic Load - to match the Natural Frequency of the glass. Then, the Acoustic Power is increased until the glass fails. A stroboscopic light - in a slightly different frequency - helps visualizing Mode Shapes.

As the last Experiment shows, not only Mechanical Loads can make structures vibrate. Aerodynamic and Magnetic Loads are examples of different types of Excitation.

INSIGHT #1

In Linear Dynamics, the Frequency of the Response and Excitation must be equal. Therefore, Steady State Excitations can be used to visualize the Mode Shapes of a Structure.

INSIGHT #2

Many have engraved in their minds that, once a structure reaches Resonance, it will fail. That's not true! As the Acoustic Experiment showed, the Power of an Excitation is also a crucial factor to determine failure.

WHAT'S NEXT?

As I told, every Project starts from its End. So, in the next Part, I'll be speaking more about Modal Tests. But I guess you already figured out one way of doing them.

If the Structure has a Linear-Elastic behavior, we can use a Steady State Load to obtain Mode Shapes. But we have to make sure the Excitation has enough Power - or Energy - to generate a Response that we can Measure.

I'll finish with a video of the X-56 Vibration Test - done by NASA Armstrong. I'm sure you'll be understanding a lot of what they are speaking about.

Again: if you liked the Article, if I did a mistake or if you have any suggestion, please, leave a Comment. Your Feedback is important to improve the continuation.