An Overview of the Exterior Matrix Method
Document Type
Article
Publication Title
Complex Analysis and Operator Theory
Abstract
The Exterior Matrix Method (EMM) is a general technique for computing asymptotically the eigenfrequencies for the vibrations of serially connected elements, each of which is governed by a system of four (or more) first order equations. The idea behind the technique is to lift the transfer matrices into a higher dimensional exterior algebra space, where it is safer to make approximations. But we can bypass the transfer matrices altogether to determine a system of six first order equations that the columns of the exterior matrix satisfy. We then only need the approximate solutions to this system to construct the approximate exterior matrix. Hence, we can find the approximate eigenfrequencies of the structure, even if the original system of equations was intractable. Finally, we demonstrate a method for finding the eigenfunctions using just the Exterior matrices, bypassing the transfer matrices altogether. We will use the Euler–Bernoulli and Timoshenko beams, as well as the taut inclined cable problem as examples.
DOI
10.1007/s11785-023-01442-9
Publication Date
11-1-2023
Recommended Citation
Paulsen, William, "An Overview of the Exterior Matrix Method" (2023). Faculty Publications. 4.
https://arch.astate.edu/scm-mathfac/4
Comments
To read this article, please send a request through InterLibrary Loan.