Recent content by Chrono G. Xay

The picture I uploaded is giving me errors. Let me try that again…

Here’s a screenshot of the graphed function (very slightly altered- LaTex below), where ##n = 6##, ##a = 3##, and ##b = 5##: $$y_1(x) = \frac{\left|{0.5\left[a - sin\left({nπx + \frac π 2 }\right)\right]} \right| sin\left({nπx + \frac π 2}\right)+\left(a-1\right)} {ab}$$ Where ##a ≥ 2## and ##b...

The annulus (“rim”) clamping the circular membrane over its cylindrical shell has a number of bolts ‘n’ positioned equidistantly around its perimeter. I’m guessing that the amount of transverse strain at those bolts would be where we might reasonably assume to be zero. When I was first trying...

Look up what ‘progressive tension’ is and why it is (because it’s the motivation behind the construction of multi-scale guitars). By comparison the tension is very unbalanced.

On a good quality instrument I expect more of the twisting or warping will arise from particularly lopsided tension on the neck owing to the strings, the current tuning, and how the instrument has been setup. (On a related note, I’m curious to engineer a truss rod with a lateral axis of...

It’s been at least a few years since I’ve added to this thread. Starting with the linearized equation you gave earlier for ##Δf## and substituting in the unconverted equation for initial tensile force $$F_0 = {μ\left(2Lf_0\right)^2}$$ as well as $$Δf = f - f_0$$ we can obtain $$f_0 = \frac {EAα}...

It’s for that very reason that when lowering the pitch of a drum you intentionally take the pitch slightly lower then what you want it, then tune it *up* to where you actually want it. 😊 The same is done for guitar strings. The rest of it will basically work itself out on its own once someone...

I’m interested in them because they’re a continuous portion of the membrane; as the rim pulls down on the hoop, which is clamped to the edge of the membrane’s collar, naturally the length of the collar affects the amount of elongation experienced until the desired musical pitch (and therefore...

Consider the picture shown at the top of this article, titled ‘Anatomy of A Conga’, particularly the part called “Drumhead Collar (Leg)”, noting the triangular shape of the collar outside of the “crown”, where the remaining length wraps over the “Drum Shell Bearing Edge”...

This is what I think I’ve come to understand so far: Starting with what I’m going to call an oscillation basis, ##ω##, defined as: $$ω = \frac {2πf_0} {J_0 \left( \frac 2 {D_{speaking}} α_1 \right)}$$ We then get our stress basis, ##σ##, defined as: $$σ = \frac {\left( ωD_{speaking} \right)^2}...

Oh, of course! We were talking about that relation earlier.

##u \left( σ \right)## is a function of radial stretching in response to stress.

In that case, what I’m thinking needs to be done is to seek a solution where one of the last steps look something like $$D = \int_0^σ u\left(σ\right)~dσ$$

1. Can anyone point me toward publicly-available research papers which examine the mechanical properties of spincast membranes, specifically Tensile Strength, Young’s Modulus, and Poisson’s ratio? 2. How doable might it be to spincast a membrane about 0.2m across and 0.076mm tall? What I am...

I was reading back over these two posts of yours, and I wanted to double-check something with you, just because not everyone is familiar with acoustic drums: This (https://en.m.wikipedia.org/wiki/File:Anatomy_of_a_Drumhead.jpg) is the physical system you were picturing when you wrote the above...