Non-stationary vibrations of a thin viscoelastic orthotropic beam Original Research Article

Non-stationary vibrations of a thin viscoelastic beam with orthotropic material properties are solved in this work. Concretely, analytical and numerical solutions of the problem of a finite simple supported beam transversely excited are presented. The analytical solution of the problem solved is derived based on the approximate Timoshenko’s beam theory and the discrete model of the generalized standard viscoelastic solid is used for the description of beam viscoelastic properties. Spatio-temporal functions describing distribution of beam deflection and slope of the beam represent the main results of this work. Moreover, the problem is solved numerically using FEM and the corresponding results are presented, as well. The comparison of results obtained shows excellent correspondence between analytical and numerical solutions and the ability of Timoshenko’s beam theory to describe non-stationary wave phenomena also for short times and in the immediate vicinity of external excitation.