  A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix
string problem is presented. Three ramifications of the approach are developed:
(1) motivated by an analogy with the Camassa-Holm equation a class of
isospectral deformations of the beam problem is formulated; (2) a reformulation
of the matrix string problem in terms of a certain compact operator is used to
obtain basic spectral properties of the inhomogeneous matrix string problem
with Dirichlet boundary conditions; (3) the inverse problem is solved for the
special case of a discrete Euler-Bernoulli beam. The solution involves a
non-commutative generalization of Stieltjes' continued fractions, leading to
the inverse formulas expressed in terms of ratios of Hankel-like determinants.
