Another consideration when building my suspension bridge was harmonic resonance. While harmonic resonance was not completely to blame for the failure of Galloping Gertie (http://www.wsdot.wa.gov/tnbhistory/Connections/connections3.htm), I decided to address the problem because it could be an issue. After all, the bridge was bound to be a little bouncy, so why make it worse?
All objects have a frequency or a set of frequencies with which they will naturally resonate when disturbed in some way – be it plucking a guitar or stepping on a bridge deck. Each of these natural frequencies is associated with a wave pattern. When the object resonates at one of its natural frequencies, it vibrates in a manner so that a standing wave is formed within the confines of the object.
A set of standing waves, in a “container” of a specific length. This set of waves is called a harmonic series, the grey dots are the nodes. (illustration by Marvin Denmark)
Harmonic resonance refers to the multiples of the strongest resonance of, in this case, a mechanical system. Resonance is the tendency of the system to absorb more energy when its oscillations match the system’s natural frequency of vibration. Resonance can cause swaying motions, but there are ways to reduce those motions. Since this was just an 80-foot long bridge, resonance was not a serious concern, but I decided to use one trick to prevent it from waving “on its nodes.”
In the case of resonance for this bridge, the waves will bounce back and forth between two boundaries: the posts. Nodes are always at equally spaced intervals where the wave amplitude (motion) is zero. The points where the cable connects to the post are two nodes. There is a possibility for one node in the middle, at third points, at quarter points, and so on, as seen in the previous drawing showing standing waves. The more excitation, the more nodes will potentially form.
I decided to space the suspenders so that they were not positioned on the nodes of the bridge span. I determined the exact points on my string model, then just moved the suspenders a couple of inches over to avoid the nodes.
Drawing of the suspenders with measurements. (illustration by Marvin Denmark)
I assembled everything on dry land according to my plan so that I could tweek things fairly easily. The final product doesn’t bounce much, unless two people and a dog are all walking on it at the same time. Or maybe a bobcat. But at least my bridge doesn’t gallop!
You can read more in my book, Building a Small Cable Suspension Bridge. There is a link to purchase it on my website: http://www.wildcatman.com.
Images, diagrams, and text copyright 2013 by Marvin Denmark unless otherwise noted. Please do not copy and post my content anywhere without my permission. Thank you.