Three?dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

We consider three-dimensional elastic frames constructed out of Euler–Bernoulli beams and describe a simple process generating joint conditions the geometric description frame. The corresponding differential operator is shown to be self-adjoint. In special case planar frames, decomposes into direct sum two operators, one coupling out-of-plane displacement angular (torsional) other in-plane with axial (compression). Detailed analysis examples presented. actively exploit symmetry present in decompose by restricting it onto reducing subspaces irreducible representations group. These “quotient” operators are capture particular oscillation modes