  We consider three-dimensional elastic frames constructed out of
Euler-Bernoulli beams and describe extension of matching conditions by relaxing
the vertex-rigidity assumption and the case in which concentrated mass may
exists. This generalization is based on coupling an (elastic) energy functional
in terms of field's discontinuities at a vertex along with purely geometric
terms derived out of first principles. The corresponding differential operator
is shown to be self-adjoint. Although for planar frames with a class of
rigid-joints the operator decomposes into a direct sum of two operators, this
property only holds for a special class of the proposed model. Application of
theoretical results is then discussed in details for compact frames embedded in
Euclidean spaces with different dimensions. This includes extension of the
established results for rigid-joint case on exploiting the symmetry present in
a frame and decomposing the operator by restricting it onto reducing subspaces
corresponding to irreducible representations of the symmetry group. Derivation
of characteristic equation based on the idea of geometric-free local spectral
basis and enforcing geometry of the graph into play by an appropriate choice of
the coefficient set will be discussed. Finally, we prove the limit conditions
in parameter space which results in decomposing of vector-valued beam
Hamiltonian to a direct sum of scalar-valued ones.
