  Polymers are ultra-versatile materials that adapt to a myriad of
applications, as they can be designed appropriately for specific needs. The
realization of new compounds, however, requires the appropriate experimental
characterizations, also from the mechanical point of view, which is typically
carried out by analyzing the vibrations of beams, but which still have some
unclear aspects, with respect to the well-known dynamics of elastic beams. To
address this shortcoming, the paper deals with the theoretical modelling of a
viscoelastic beam dynamics, and pursues the elucidation of underlying how the
flexural vibrations may be affected when an axial preload, compressive or
tensile, is applied. The analytical model presented, is able to shed light on a
peculiar behaviour, which is strongly related to the frequency dependent
damping induced by viscoelasticity. By considering as an example a real
polymer, i.e. a synthetic rubber, it is disclosed that an axial preload, in
certain conditions, may enhance or suppress the oscillatory counterpart of a
resonance peak of the beam, depending on both the frequency distribution of the
complex modulus and the length of the beam. The analytical model is assessed by
a Finite Element Model (FEM), and it turns out to be an essential tool for
understanding the dynamics of viscoelastic beams, typically exploited to
experimentally characterize polymeric materials, and which could vary
enormously simply through the application of constraints and ensued preloads.
