The inverse problem for the vibrating beam. (English) Zbl 0542.73087

The problem of constructing the continuous mass and stiffness distribution of a vibrating beam from the knowledge of spectral data is the so-called inverse problem for the beam. In this paper, the beam is modelled by a system of rigid rods joined together by rotational springs and with masses at the joints. One end of the beam is clamped and the other is either free or pinned or sliding or clamped. It is shown that the resonant and antiresonant frequencies of the system may be almost completely ordered. Necessary and sufficient conditions are found that these frequencies must satisfy to correspond to an actual system, with positive parameters. Two stripping procedures are devised for the determination of these system parameters, from a knowledge of certain frequency spectra.
The paper is of interest to both applied mathematicians and engineers.
Reviewer: G.Ramaiah


74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
35R30 Inverse problems for PDEs
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