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**Sufficient conditions for the solution of the inverse problem for a vibrating beam.**
*(English)*
Zbl 0629.73040

The author studied the same problem in the paper reviewed above (Zbl 0629.73039). In the present work the author takes again the question and discusses the necessary and sufficient conditions for the existence of a solution to the inverse eigenvalue problem for a vibrating beam. The inverse problem consists in determining the density and the flexural rigidity from spectral data, which consists either of the spectra or of impulse response information. Here the latter type of data are used as starting point. Necessary and sufficient conditions are studied and discussed particularly relatively to the proceedings and results of G. M. L. Gladwell [see the citation in the above reviewed article)]. One concludes that the different starting points for solving the inverse problem under consideration, namely the three spectra approach and the impulse response approach are equivalent: one can see this fact from certain formulae which are given by the author in this paper.

Reviewer: A.Pignedoli

### MSC:

74H45 | Vibrations in dynamical problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

34A55 | Inverse problems involving ordinary differential equations |

34L99 | Ordinary differential operators |