Let’s Change The Way You Think Structures Vibrate
In many aspects of our lives we deal with vibrating structures. Whether it is your car going down the road or your office high rise blowing in the wind (Yes, they really do…), all structures move when excited by something. By excited I simply mean pushed or nudged. In a car, for example, hitting a pothole or a speedbump can excite the car’s structure and then the car will respond. What I will hopefully help you understand is that there is not ONE way in which the car will respond. All structures respond in MANY different ways. The response you will see (or hear) in a given scenario depends on the structure as well as the exciting force (e.g. is it short like a speed bump or long like a kid jumping up and down in the back seat). To start to understand this, we need to talk about mode shapes.
Mode Shapes
All structures naturally want to move in what we call mode shapes. These are shapes determined by the mass, damping, and stiffness of the structure. Note by structure I mean anything like a building, your kitchen table, or a car tire. Let’s use a car wheel (i.e rim) as the example from here on out. This car 20×8.5 rim to be specific:
We can do some fancy computer work and get a general idea of what the first 8 mode shapes look like (below). These are the shapes that the rim naturally wants to make. The mode shapes all occur at certain frequencies. For example, the first mode wants to happen at 281 Hz according to our computer model. But there are many shapes and corresponding frequencies! How do we know which shape a structure is making in real life? The answer to that question is that at any given time your rim is moving in ALL of these shapes, but one or some of the shapes are more pronounced or obvious.
Mode 1 – 281 Hz
Mode 2 – 283 Hz
Mode 3 – 579 Hz
Mode 4 – 581 Hz
Mode 5 – 723 Hz
Mode 6- 959 Hz
Mode 7 – 960 Hz
Mode 8 – 1,319 Hz
Okay, so we now know that all structures have these mode shapes that they want to make and those shapes happen at certain frequencies, but how do I know what is causing my vibration? The answer to that question is that you need to figure out what is exciting your structure at the frequency of a mode shape. In the rim case, if you have a worn out brake rotor (i.e. disk that your brake pads clamp on) then that could be creating an impact force that happens at 281 times/second or Hz. This would then cause your rim to want to move in its first mode shape, because your excitor is exciting the frequency of the first mode, 281 Hz. So if you want to fix this vibration, you need to fix your brake rotor so that it does not excite 281 Hz. Knowing the mode shapes and their frequencies helps you narrow down what could be causing your vibration to only items that excite at mode shape frequencies.
Conclusion
The main take-a-way from this is that all structures have many mode shapes they want to move in and at all times they are moving in all of those shapes, but one or some of those shapes may be dominant. So if you have a vibration issue, you need to figure out what is exciting the structure and see if you can either A) change the structure’s mass or stiffness properties to change the mode shape frequencies B) Change the amount of damping so the response is not so high or C) change the excitor such that no mode shape frequencies are being excited by that excitor.
Post comments below if you have any questions or want more clarification!
-Troy
www.TroyBouman.com
Bonus: Finding mode shapes in real life!
The models I showed above were all generated from a FEA software, but you can also find mode shapes experimentally using modal analysis. This allows us to go to go any structure already in operation and determine what shapes it wants to make and at what frequencies to try and decrease its vibration. Here are the first 7 modes of the rim found experimentally. The picture below is an example of one testing point (note there were 91 points in our testing). We hit the rim with the fancy hammer and measured the response with an accelerometer.
Here are the resulting shapes:
The power of being able to find mode shapes experimentally is that we can figure out how a machine is actually moving in real life so that we can determine the best way to stop the movement. If you have an old machine, modeling it in a FEA software may not make sense, because all of the joints, gears, mounts, etc… are worn and the system properties have changed over time. So finding the mode shapes experimentally is the only way find the correct frequency of the each shape.
-Troy
www.TroyBouman.com