Efficient computation of coupled bending and torsion vibrations of slender structures with an axially moving eccentric load. Issue 1 (14th December 2021) - Holl, Helmut J.; Keplinger, Lukas
Abstract: Frequently slender structures are excited by moving loads and show the corresponding transient vibrations. A model is derived using a simply supported Bernoulli‐Euler beam and the coupled bending and torsion vibration equations are derived. An analytical solution of the decoupled partial differential equations is derived based on the eigenmode expansion considering the boundary and initial conditions. For the pure bending and the pure Saint‐Venant torsion the analysis is performed and the beam vibrations are calculated. The coupled bending and torsion deformations are computed using a modal transformation, where it is essential that the eigenmodes are the same for both kinds of vibrations. The resulting modal decoupling yields two separated ordinary differential equations in time with the assumed constant velocity of the axially moving excitation load. Closed form solutions are used which show a very good convergence. A transformation into the original coordinates results in the solutions of the coupled equations. The results are plotted in a dimensionless form. The evaluation and comparison with a suitable numerical calculation using a finite element model shows a good agreement of the results. It turns out that a fine discretization is necessary and the computation effort for computing the transient dynamic solution is very much higher.