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

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. (C) 2001 Elsevier Science Ltd. All rights reserved.