Inverse eigenvalue problem for a circular membrane

Rick P. Millane

doi:10.1117/12.139048

29 December 1992 Inverse eigenvalue problem for a circular membrane

Rick P. Millane

Author Affiliations +

Proceedings Volume 1767, Inverse Problems in Scattering and Imaging; (1992) https://doi.org/10.1117/12.139048
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

The problem of determining the density distribution of a circularly symmetric elastic membrane, fixed on the edge, from its frequencies of free vibration, is examined. An asymptotic analysis implies that a density function that is a small perturbation from a homogeneous membrane is determined, up to a finite number of parameters, by two infinite spectra of appropriate angular orders. An algorithm for reconstructing the density from the spectra is presented. The results are illustrated by numerical simulations.

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Rick P. Millane "Inverse eigenvalue problem for a circular membrane", Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992); https://doi.org/10.1117/12.139048

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