Determination of the form of attachment of a rod using the natural frequencies of its flexural oscillations

I. Sh Akhatov, A. M. Akhtyamov

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

The inverse problem of finding the form of the attachment of one of the ends of a rod, which is inaccessible to direct observation, from the natural frequencies of its flexural oscillations is considered. A theorem on the uniqueness of the solution of this inverse problem is proved and a method for establishing the unknown boundary conditions is indicated. An approximate formula for determining the boundary conditions is obtained using a finite set of natural frequencies (it is assumed that these natural frequencies can also be specified approximately with a certain degree of accuracy). The use of just the first non-zero natural frequencies is found to be essential here.

Original languageEnglish
Pages (from-to)283-290
Number of pages8
JournalJournal of Applied Mathematics and Mechanics
Volume65
Issue number2
DOIs
Publication statusPublished - 2001
Externally publishedYes

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