Exterior Matrix Method
The Exterior Matrix Method is a means of finding the eigenfrequencies for
a sequence of 4th order PDE's which are coupled, that is, the end points for
one equation becomes the initial conditions for the next. Normally, the
transfer matrix method is used, where a 4 by 4 matrix is produced corresponding to each differential equation, and then the matrices are multiplied together.
However, for the final end conditions, a 2 by 4 matrix and a 4 by 2 matrix must
also be multiplied, and a final 2 by 2 determinant must be taken. It is this
final determinant that gives us the headache.
To download the notebooks, right-click on the link and select "Save as".
These notebooks were created with Mathematica 5.2 for Windows, but it will be
compatible with any fairly recent version of Mathematica will work. If you do
not have Mathematica, you can download the expanded version of the notebook,
and use MathReader to view the file. But the unzipped expanded version is 21MB.
Download expanded Mathematica notebook (zipped)
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