Effect of an axial pre-load on the flexural vibrations of viscoelastic beams

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 modeling of a viscoelastic beam dynamics and pursues the elucidation of underlying how the flexural vibrations may be affected when an axial pre-load, compressive or tensile, is applied. The analytical model presented is able to shed light on a peculiar behavior, which is strongly related to the frequency-dependent damping induced by viscoelasticity. By considering as an example a real polymer, that is, a synthetic rubber, it is disclosed that an axial pre-load, 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, 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 pre-loads.