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 end s of a rod, which is inaccessible to direct observation, from the natural f requencies of its flexural oscillations is considered. A theorem on the uni queness of the solution of this inverse problem is proved and a method for establishing the unknown boundary conditions is indicated. An approximate f ormula for determining the boundary conditions is obtained using a finite s et of natural frequencies (it is assumed that these natural frequencies can also be specified approximately with a certain degree of accuracy). The us e of just the first non-zero natural frequencies is found to be essential h ere. (C) 2001 Elsevier Science Ltd. All rights reserved.