On the Scattering of Waves in a Non-Uniform Euler-Bernoulli Beam

A scattering theory for waves in non-uniform Euler-Bernoulli beams is developed and shown to be analogous to the corresponding theory for longitudinal waves in rods. Both continuous and abrupt scattering are considered, and the relevant differential equations and matrices are derived. It is shown in particular that if the beam is such that the product of its area of cross-section and its second moment of area is constant, then it is, in a certain sense, equivalent to a rod. In that case known procedures for reconstructing a rod from two spectra can be applied, with the necessary changes, to the beam.