Eigenfrequencies of the three-dimensional Euler-Bernoulli beam system with dissipative joints (Q1904867)

We compute the transfer matrices to find the eigenfrequencies for the vibrations of the general non-collinear Euler-Bernoulli or Timoshenko beam structure with dissipative joints. We allow the structure to be three-dimensional, and thus we consider all types of vibrations simultaneously, including longitudinal and torsional vibrations. The structure consists of any number of beams joined end to end to form a chain. We show that asymptotic estimates can be used to find the eigenfrequencies approximately.