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Inverse spectral problems for inhomogeneous elastic cylinders

✍ Scribed by Lev G. Steinberg

Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
595 KB
Volume
38
Category
Article
ISSN
0374-3535

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✦ Synopsis

The goal of the paper is to formulate the inverse spectral problems for a determination of elastic moduli and to develop a method of their solution. These types of problems always arise when one tries to determine moduli in inhomogeneous materials using spectral data which are received from an experiment of excitation of free oscillations. Our treatment of the problems is within the framework of linear elasticity and is based on the Levitan and Marchenko's theory of Sturm-Liouville inverse problems.

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The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnis