Abstract
It has long been known that two scaling factors and three spectra, corresponding to three different end-conditions, are required to determine the cross-sectional area
A(x)
and second moment of area
I(x)
of an Euler-Bernoulli beam. What has not been known are the necessary and sufficient conditions on the spectral data which will yield
positive
functions
A(x), I(x)
. Such a set of conditions is derived in this paper.
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