Reconstructing the cross-sectional area of an axially vibrating non-uniform rod from one of its mode shapes

Author Type

Outside Researcher

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

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

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