A solution method for Euler–Bernoulli vibrating discontinuous beams

The eigenvalue problem of Euler–Bernoulli discontinuous beams is addressed. Specifically, for stepped beams with internal translational and rotational springs, it is shown that a formulation of well-established lumped-mass methods employing exact influence coefficients is readily feasible, based on appropriate Green’s functions yielding the response of the discontinuous beam to a static unit force. The latter are not available in the literature; here they are derived, in a closed form, for arbitrary boundary conditions. Advantages of the proposed eigensolution are pointed out and future developments are also discussed.