Longsword dynamics, FEM Analysis Eigenmodes
Hello dear friends,

I've done some further study about the dynamics of a longsword. Some old information can be found here [1]. The idea, that the vibration nodes of the first elastic mode (first picture) are influencing the position of the blade, where the most energy can be transfered to the target is well known. But thinking of a 3D item, a sword as an infinite number of such eigenmodes. Of course only the low ones are interesting. Every Eigenmode comes with its own frequency. The first mode of my model has a freqency of about 16 Hz, humans certainly can't hear the sound of this vibration.

But we are able to hear the second Eigenmode (second picture). Just fetch your longsword, hold one of the three nodes of no vibration and bump the blade with a rubber gum where the maximum amplitude is (green sections). This should give a sound with a frequency about 40 Hz (in reality its a mix of lots of modes, but try to stimulate the second mode).

The third Eigenmode (and that is what I want to dicuss) is also important to the position on the blade where the most energy can be transfered when hitting a target. The third picture shows that the vibration occurs in a 90 degree rotated plane in contrast to the first and the second Eigenmode. You could also test this while holding a node (blue section on the picture) and bumping the blade within the green section (hit the edge, not the surface). You can hear a sound which is about 60 Hz. I verified this on my own with two differend longswords and a final FFT-analysis of the sound (getting the frequencies out of a sound).

My idea: Is the third mode (and the position of the nodes of no vibration) important to the position of the blade, where the most energy can be transfered to the target? Is the third mode even more important, because an ideal hit stimulates only modes within the plane where the third mode occurs (imagine your hit is perfectly perpendicular to the target)?

Best regards!
Tom Guder

PS.: There is some work in progress about pivot points with FEM.

[1] http://www.myArmoury.com/talk/viewtopic.php?t...hlight=fem

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Good work!

The influence of these modes of vibration on the cutting performance is something that is not settled. It seems to depend on the target. An argument has been made that the energy stored in such modes for realistic amplitudes of vibration is actually small compared to the total energy available for cutting. I wonder if the reason this matters in some cases is not rather that vibrations end up causing friction forces and therefore end up dissipating the energy. If that is the case, it's indeed the flat-to-flat modes that matter...


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