Visualization of Drumhead
3-D Representations of Clamped Circular Membrane  
 

  • Radial Solutions are Bessel Functions Jm(zmn· r/a)
          where zmn is n-th zero of Jm(x)
  • Radial Solution will have n zeros
  • Angular Solution will have m cut lines
     
     
  • Mathcad Used to Calculate and Display 3-D Surface
  • Surface can be Rotated and Animated in Real Time
 
Chromatek Coloration mapped to Vertical Displacement

 
Chromatek Coloration mapped to Displacement and Depth
 
Surface Plots Based on Vertical Displacement
m=0 , n=1

 m=1 , n=1

 m=2 , n=1

m=0 , n=2

 m=1 , n=2

 m=2 , n=2

m=0 , n=3

 m=1 , n=3

 m=2 , n=3

Click on any Figure to View Animation (1.5 MB AVI Files)  
 
 
Surface Plots Based on Depth and Displacement
m=0 , n=1
 m=1 , n=1
 m=2 , n=1
m=0 , n=2

 m=1 , n=2

 m=2 , n=2

m=0 , n=3

 m=1 , n=3

 m=2 , n=3

Click on any Figure to View Animation (1.5 MB AVI Files)  
 
 

Mathcad 8 Worksheets
  • Worksheet to Generate Chromatek Colormap
  • Worksheet To Plot Drumhead in 3-D
        Chromatek Coloration mapped to Vertical Displacement
  • Worksheet To Plot Drumhead in 3-D
        Chromatek Coloration mapped to Displacement and Depth
 
 
 
 
Electronic Copy of Document:
http://www.gac.edu/~huber/chromatek/drumhead.htm

Revised: 01-Aug-2000 by Tom Huber
Physics Department, Gustavus Adolphus College