4/19/2023 0 Comments Sword dynamics calculatorHowever, it shows what is sufficient to obtain the observed effects. I remain convinced that the interest of such simulation is limited, because the perceptible results (dynamics, nodes of the first mode of vibration) are easily measured on swords. Modes of vibration of the bare blade, virtually removing cross and pommel. For example, the pommel and cross can be virtually removed. Interesting virtual experiments can be done with this program. It might indicate that my measurements were not perfectly accurate, which is likely given the approximation made especially on the cross-section shape. This uniform change does not moves the nodes or pivot points at all (this is a mathematical property of the model I use). My first simulation was giving a mass of 950g, while my sword weights 1009g. I had to adjust the density slightly to account for the mass of the sword. The blade node is exactly right, the hilt node is a bit more difficult to measure, but seems to be spot-on as well. The harmonic nodes are precisely computed, from what I can see. For each mode, I made two symmetric curves, that indicate the deformation of the sword bending one way, then the other. I plotted only the three first modes to keep the figure clear. The curves are scaled according to the energy of the sword when it vibrates in that mode: the higher the mode, the less ample the vibration becomes. The first mode, that is used to determine the blade node and hilt node, is in black. The curves represent the modes of vibration. The straight black line is the axis of the undisturbed sword. The modes of vibration, computed here in the flat to flat plane, which is the one we are able to observe. I was then able to compute an approximate mass distribution, and rigid body dynamic properties: I entered all this into my program, along with average values of density and Young modulus for steel, aft and forward positions on the grip (to compute aft and forward pivot points). upper part of the blade (5 elements), not fullered.middle part of the blade (10 elements), the fuller stops here.I ended up with 7 parts for the sword, over which I assumed the variation were linear, that I further subdivided in elements roughly according to their length: I didn’t want to go through the trouble of unmounting the sword so I made some reasonable guess for the tang based on what I remembered. I measured as precisely as I could cross sections across the blade, as well as the pommel and cross-guard. To be honest, I was expecting a more or less spectacular failure. That is an appropriate model to simulate the very relaxed grip that is assumed when looking for vibration nodes.īeing satisfied with the behavior on basic test cases (uniform bar, simple taper, and so on), I decided to go for something a bit less obvious and tried to simulate a real sword of mine: my Angus Trim type XI. In addition to rigid-body dynamic properties (mass, center of gravity, pivot points), it finds the modes of vibration, assuming that the sword is not constrained by anything. The program solves the equation from the model using a 1D finite elements approach. I chose a simple model for the sword, in fact one of the simplest models for slender, flexible beams (the name of the model is Euler-Bernoulli), that allows a varying cross-section along the length of the beam. I have built a small Scilab program to simulate blade harmonics and dynamic properties (pivot points, center of gravity, mass), taking as inputs parameters from the materials (density, elasticity) and geometry (lengths and cross-sections). I happen to have worked on that a few years ago, and this post desribes the results I have obtained. Over the years the topic of the simulation of the properties of swords has come up a number of times.
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