Can We Predict Damping Coefficient of a String Using Mathematical Simulation?

[Chrono G. Xay]

Is it possible to predict the damping coefficient of a string using a mathematical simulation that included the string's diameter, length, frequency (and therefore tension), material density, and elastic modulus (if not also its Poisson's ratio) as opposed to simply looking at the amplitudes of each successive wave? I'm guessing that It would be even more accurate to factor in modes of vibration that are not just the fundamental, as well as how these modes are excited differently based upon where along the string's length it is initially deflected.

I would like to think that we can, but then again do I not also need the density of the atmosphere--assuming it's air, if not a vacuum--and the string's velocity (meaning I would probably need to know the distance of the string's initial transverse displacement, and therefore the restoring force of the deflected string?

I haven't been to find articles that I really understood and didn't just contain cursory knowledge:

http://hyperphysics.phy-astr.gsu.edu/hbase/oscda.html#c2

https://en.m.wikipedia.org/wiki/Damping_ratio

 

[Simon Bridge]

Short answer: no.
Pretty much for the reasons you state: too many variables.
You end up using catalogs of material properties to make guesses, then refine for the specifics.
If you need a particular damping coefficuent, you build that part to be close and tuneable.

 

[Nidum]

Also the damping coefficient for an isolated perfect string is not a very useful thing to know even if you could work it out . A string in an actual instrument will behave quite differently anyway since it is interacting with the complex response of the sound box and other components .

 

[Nidum]

http://large.stanford.edu/courses/2007/ph210/pelc2/http://www2.eng.cam.ac.uk/~jw12/JW%20PDFs/Guitar_II.pdf

 

[Spinnor]

I would think air damps the string the most. An experiment to test this,

http://www.usc.edu/CSSF/History/2009/Projects/J1917.pdf

From,

https://www.google.com/search?sourceid=chrome-psyapi2&ion=1&espv=2&ie=UTF-8&q=how long will a string vibrate in a vacuum&oq=how long will a string vibrate in a vacuum&aqs=chrome..69i57.12526j0j8

Edit, and I would be partially wrong. As the test above shows air is most important for larger strings.

 

[Chrono G. Xay]

Sometimes the best model we can do is the ideal model: An instrument with no resonating chamber whose body, neck, and headstock are immovable, in an atmosphere (i.e. air) of static temperature, pressure, humidity, and therefore density, and viscosity. I will even look at the change in the force of gravity with a change in height above sea level if I need to. At this point in time I am honestly not interested in how the string interacts with the body, but how the string interacts with the atmosphere itself. The guitar's body, neck, and headstock are a different elements that come together. Guitars vary a lot more than strings do.

I'm honestly not afraid to do a little lookup for material values if need be. I've done it before for projects very much related to this.

 

[Nidum]

https://courses.physics.illinois.edu/phys406/Student_Projects/Fall00/STreharne/STreharne_P398EMI_Final_Report.pdf

 

[Chrono G. Xay]

The hope- the goal of all of this is so that as people *do* write equations for the behavior of the neck, or the headstock, or the truss rod, the body, and the resonating chamber, they can just drop this one in place and be done that much faster, kind like making a seatbelt so that when there is need of one the other person can just take it use it, instead of having to piece one together themselves.