Mathematical modeling - how to calculate the displacement at any point in a membrane

I'm trying to calculate the displacement of a wall at any point due to a point source of vibration. The vibration is considered to be directly perpendicular to the surface of the wall, for calculation purposes.

Input: random force applied to some point (call it white noise)

Output: Displacement at any other part of the wall (located (x,y) from the original point)

I assume that the displacement will at a simple level be related to some K(x,y). The relationship is probably K/(x^2 + y^2), I just need to figure out what goes into K

As far as I can say, the stiffness of the material will increase the speed and distance with which displacement waves travel, and decrease the total displacement.

Also, things like standing waves with the borders of the wall, vibrational characteristics of the material, and others come into play. I'm not really sure how to model all these things.

Can anyone give me some more input into what I should be considering, or maybe some actual equations that can help me relate the material properties of the wall to the displacement at a specific location?

Thanks.

• This is really a physics question, not a mathematics one. Look for books on elasticity theory - they will have answers to all of your questions. – j.c. Jan 15 '10 at 21:36
• One thing you might look at to get started is the Green function for the wave equation. – Steve Huntsman Jan 15 '10 at 21:52