Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
Publication Status
Version of Record
Abstract
It is shown that the cross-sectional area of a non-uniform axially vibrating rod can be reconstructed from one of its mode shapes, and that the solution, up to a scale factor, is unique. The conditions, which allow construction of a physical rod with positive smooth cross-sectional area, are given. The problem is addressed for the discrete and the continuous models of the rod. Examples demonstrate the various results.
First Page
1583
Last Page
1596
DOI
10.1098/rspa.2003.1214
Publication Date
6-8-2004
Recommended Citation
Ram, Yitshak M. and Elishakoff, Isaac, "Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes" (2004). Faculty Scholarship. 438.
https://digitalcommons.fau.edu/faculty_papers/438