MOLA Mode Shapes

In General ...

The links presented below will show you various mode shapes of MOLA when it is vibrating at its natural frequencies. Please keep in mind that all these pictures are extremely exaggerated. If a view shows one part of the model passing through another part, it is not really happening. In fact, if any part actually touches another part while it is vibrating, then we have failed in our design and analysis. Generally, when these things vibrate, we're talking movement of maybe a millimeter or less.
For those of you who already understand what mode shapes are and just want to see how MOLA reacts, then select from the bullets below. If you don't understand what you're looking at, then go to the explanation a bit farther down the page.

You can look at an exploded view of the MOLA Finite Element Model if you need to recall the parts of the model.

If you are using Netscape Navigator 2.0 or later, OR have an animated GIF viewer, then you can view several of the mode shapes in action.

What are Modes and Mode Shapes?

Let's think of this using an example we all are familiar with.

Pretend you're in a car sitting at a stop sign. When it's safe to go you accelerate. As you speed up, you notice your rear-view mirror begin to shake. As you increase your speed, the mirror stops shaking but your dashboard begins to shake. Go even faster and the dashboard quits shaking but then your steering wheel starts to shake.

All of these are examples of Normal Modes -- what you might call Natural Frequencies. Frequency is measured in Hertz (Hz) and is in units of Cycles Per Second. Each time your mirror goes back and forth once, that is a cycle. Measure the number of times it goes back and forth every second and you have the frequency. Some things move very slowly, like a pendulum (one or less Hz); other things move quickly, like a bee's wings (hundreds of Hz); while still others move extremely fast, like a high note on a musical instrument (thousands of Hz). When you think about sound, the lowest frequency humans can hear is about 16 Hz, while the highest is somewhere around 20,000 Hz. The inverse of frequency is the Period, which is the time it takes to complete just one cycle. But we don't use the period much in our work.

Everything has an infinite number of natural frequencies. We are interested in only the lowest ones. Another example is in order here. Take out your Slinky. It doesn't matter if it's bent, it will still work. (For the international crowd, a Slinky is a toy spring that is rather popular in the U.S. It walks down stairs all by itself.) Now, hold your Slinky with one end in each hand and let about half a meter sag in the middle. Next, begin slowly shaking one hand only until the middle is moving up and down. When you have it moving smoothly with only one hump, then you have found the First Mode. Next, shake your hand faster a little at a time until you can see two humps in the Slinky. When you can keep the two humps constant, you have found the Second Mode. If you're really good at this, you can move on and get the Third and Fourth Modes. With a friend and the Slinky fully extended, who knows how many modes you can find!

Just in case you don't have a Slinky handy, I've created some animated GIFs that show the various mode shapes of a 2-dimensional vertical bar, pinned at each end. To view these, you must have either Netscape 2.0 (or better) OR a viewer that displays animated GIF files. Other browers will show you the mode shape, but it will not be animated.

Mode 1 - Mode 2 - Mode 3 - Mode 4 - Mode 5 - Mode 6 - Mode 7 - Mode 8

These modes are very important to engineers because when they occur, there is a lot of energy moving into whatever structure you are looking at. It's this energy that makes the thing vibrate. If there is too much energy, then your structure will break. That makes sense because if you think about how you might try to break a wire, you would do it by bending it back and forth. Well, vibration is also moving something back and forth. So if your structure is vibrating but is not strong enough, it will break. And because there are many things that can cause a structure, like a car, to vibrate (like the engine in the car, or the bumps on the road) we have to know at what frequency the car will vibrate and make sure it never sees that frequency caused by something like the engine or the road. Or better yet, make the first mode of your structure as high as possible and you will probably not have to worry about that kind of failure. When you make a structure stiffer, then you increase the frequency.

Therefore, we need to look at structures like MOLA, find out where they have their natural frequencies. We know that the rockets on which spacecraft launch generate frequencies generally less than 50 Hz, so our structure's first mode must be greater than that. There are many other factors involved, and so our first frequency should really be higher still, but that is a good starting point.

Back to the MOLA Analysis Home Page.

Goddard MeatballThis page is maintained by Ryan Simmons, at
This page was updated on April 22, 1996.