- #1

dykuma

- 56

- 7

## Homework Statement

Not sure if this is the appropriate place to ask this question, but I didn't know where else to ask.

Anyway.

Let's assume that I have a film (or membrane) material that is stretched over some boundary, (lets assume a thin hollow cylinder). Then some constant force is applied over the surface (a pressure). Assuming the deflection is small, what is the sagitta (or depth) that the membrane is deflected by for a give material?

## Homework Equations

In this case, I've made several assumptions. First, the deflected part of the membrane is actually a very tiny slice of a sphere. As such, for small deflections I'm able to treat one surface of the membrane like the inside of a bubble (specifically the concave side of the deflection).

As such, my equations are:

Where P is some difference of pressure on either side of the membrane, Rc is the radius of curvatures, r is the radius (or half the span) of the un-deflected membrane,

For my purposes, I have no need to solve for the "sag" at the moment, as that information is encapsulated in the radius of curvature and can be easily calculated.

## The Attempt at a Solution

Obviously, with the conditions I have set, the solution to the problem is:

Anyway, the issue I am having is being able to solve this for a specific material. From what I understand, T is the surface tension of the material, but I am not sure this is always available. My guess was that:

T=E⋅t

where E is the Young's modulus, and t is the thickness of the material. However, I am not sure that is correct.

This issue is further complicated when I assume that some form of tension is already being applies to the membrane in order to stretch it. Do I need to take that into account as well?

Basically, my question is, if I have the produce sheet of a given material (like a rubber sheet), how do I obtain the value for T?