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What the Playground Can Teach Us About Resonance in Dynamics

By Altair Partner Alliance | DSA |

Kids are always happy to visit a playground. When my son turned three, the swings became one of his favorites. He always wanted to go higher and higher. At that age, he hadn’t quite figured out how to swing by himself yet and needed a push to keep going. Fortunately for me, pushing swings only require a little effort to get a significant response. In this way, swings can teach us a lot about dynamics, and in particular, resonance.

The key to resonance is that a little effort can mean a big response. Knowing how resonance works is essential because it can make or break your system. So what is resonance?

Small children need a push to get going on swings. Fortunately, resonance helps here, as small pushes over time lead to large motions.
Small children need a push to get going on swings. Fortunately, resonance helps here, as small pushes over time lead to large motions…and happy children!

Resonance is a large response to a small disturbance

In mechanical systems, a large response might mean large amplitudes of motion. Resonance is often inherently a vibration. So these large responses are in some way an oscillation – which means the external disturbances also need to be an oscillation as well.

So how does resonance work? Resonance can only occur when a system has some form of inertia as well as a restoring effect. This means a physical mass must provide inertia. The restoring effect is any kind of force that acts to bring this mass back into an equilibrium position. The specific combination of inertia and a restoring force produces a natural frequency. This natural frequency appears when the mechanical system is in motion without any dominating external force. It’s when external forces, even tiny ones, come into play at a rate around the natural frequency that you get resonance.

Swings are a perfect example of resonance

In the case of my son on a swing, he provides most of the inertia. Gravity provides the restoring effect that always tries to bring the swing back into its center position. Now all that is needed is a little push at the right moment, and with this bit of effort after a little while, he is soaring high into the sky (and typically demanding to go higher).

Another example of resonance is ship motion response

Often, the roll response of a ship can be a problem. All ships have a certain amount of inertia to them. Depending on the loadout and shape of the hull, the ship will have a certain amount of restoring effect in roll. In this case, the problem with resonance is when the frequency of ocean waves line up with the natural frequency of a ship in roll – this is when you get roll resonance.

This can create extensive roll motions or large roll accelerations – causing people to get seasick, fall over, get injured, or damage equipment on the ship. For example, the MCS Zoe lost 350 shipping containers in a rare storm that was partially attributed to roll resonance. Keeping an eye on ship motions and how big these motions get is a big concern in ship seakeeping analysis.

The MCS Zoe lost 350 shipping containers during a rare storm that resulted in roll resonance.
The MCS Zoe lost 350 shipping containers during a rare storm that resulted in roll resonance. Picture credit: Hummelhummel, Wikipedia Commons, License CC-BY-SA 3.0

Is resonance always a problem?

Resonance can be good and bad. A lot of engineering systems rely on resonance to work correctly. But resonance can also spell disaster. If minor disturbances create significant effects there will be countless opportunities to make large forces and motions, damaging equipment or causing injuries.

Damping can drastically reduce the resonant response. Back to the swing set at the playground; there is only a bit of air drag slowing things down. This tends to be an excellent example of how little effort can lead to a big response. That little effort, such as a helpful push from a parent, needs to be periodic and applied at just the right time.

Back in the marine world, there are examples of significant damping in ship motion, too. For many ships, wave radiation considerably damps pitch motion. As a result, resonance is not always a big concern for ship motions in pitch. Regardless, carefully understanding when and how a system might reach resonance is essential.

Can you always figure out resonance?

The more complex the system, the more difficult it is to figure out how resonance works and whether it is a problem. In ship seakeeping analysis, it helps to have a specific software tool that takes all the details of a ship, including the hull shape and inertia, to establish just how the system will move – and possibly resonate – in different sea conditions.

Summarizing

Resonance is when small disturbances lead to a large response. In mechanical systems, it’s a vibration effect, and so you can’t get resonance without some kind of inertia and a restoring force. Resonance is a good thing in the playground as it helps to keep my son happy without a lot of effort. But it can lead to disaster and damaged equipment if you don’t monitor it closely.

Next step

In one of the examples, we covered how resonance is a dangerous condition that can show up in ship motions. A seakeeping analysis is what helps understand just what kind of ship motion will occur in different sea states, and if resonance is a concern too. Read more on what seakeeping analysis is all about here.

– Ryan Nicoll, Co-founder and chief technology officer, DSA Ocean