[Harp-L] Description of Harmonica Reed Physics (Was: Johnston or Johnson)

[Robert Coble <robertpcoble@xxxxxxxxxxx>]

MusiCal,


The biggest problem with most papers on cantilever beam equations
is an assumption of uniform thickness of the beam. Apparently, 
there is a dearth of good papers on equations for NON-uniform 
cantilever beams. Other than Finite Element Analysis software,
such as LISA, I have not found any software to solve the mechanical
equations. I also have not seen ANY papers or software which take 
the aerodynamics into consideration.

Check out this paper:

http://www.engineeringmechanics.cz/pdf/15_1_003.pdf

"MATHEMATICAL MODEL FOR VIBRATIONS OF NON-UNIFORM FLEXURAL BEAMS"

I am NOT a physicist or mechanical engineer. The 4th-order partial 
differential equations given in the paper are beyond my limited 
knowledge of calculus and partial differential equations.

With that caveat, however, I have had the pleasure and good fortune 
to have worked with Vern Smith on a prototype reed-profiling machine. 
I had phosphor-bronze reed blanks made, cut using EDM and sized to 
Vern's specifications. I wrote some VBA code (inside an Excel 
spreadsheet) to allow reed sizing information (length and thickness) 
to be used to generate the G-codes to control the actual profiling 
(thickness) of the reed. The prototype worked (proving that the design 
concept was feasible for cutting reed profiles longitudinally) but the
prototype still had an unresolved problem when Vern ceased work on it.
I learned a lot from Vern, and am very grateful for the experience.

Two possible collaborators (physicists) are:

Michael Marino, SlideMeister
Dr. James Antaki, TurboDog (Harp-L) - Principal at TurboHarp

IIRC, Dr. Antaki worked in collaboration with Dr. Bahnson.


Another possible source for equations and discussion is:

http://www.modernbluesharmonica.com/board/board_topic/5560960/3113771.htm?page=1

Dirty-South Blues Harp forum:  wail on!>
		
			Reed failure, by the numbers


I am still interested in reed-making machines which profile the reeds
in the longitudinal direction, rather than laterally across the reed.
I understand the mass manufacturing engineering reasons for cutting 
the profile laterally on a long strip, and then punching reeds out of 
the strip. The ill-fated Harrison Harmonicas B-Radical had longitudinally 
milled reeds. There also is a chromatic harmonica designed by Franz 
Chmel that uses longitudinally milled reeds. Unfortunately, the last 
time that I checked, the price was somewhere around $14,600 for one.
I assume (without evidence) that the longitudinally milled reeds are 
not the only nor the most significant cost driver.

Good luck!
Crazy Bob