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Inverse Problem for a Vibrating Beam.
CHICAGO UNIV ILL DEPT OF THE GEOPHYSICAL SCIENCES
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The problem of inferring the flexural rigidity and density of a beam from its eigenfrequencies is considered, for the particular case in which one end is clamped. It is shown that three spectra associated with three sets of boundary conditions at the other end are required in order to insure a unique solution of the inverse problem. Furthermore, it is shown that this data set is equivalent to the information contained in the time history of the displacement and slope of the free end of the beam set in motion by a concentrated impulse.
APPROVED FOR PUBLIC RELEASE