EFFECT OF A VISCOELASTIC BOUNDARY INSET ON VIBRATIONAL CHARACTERISTICS OF A BEAM (DAMPING, DISSIPATION, EARTHQUAKE)

The effect of a viscoelastic (elastomeric) inset on the vibrational characteristics of a cantilevered beam in flexural motion is examined. The inset is placed at the support fixture of the beam. A closed form solution is obtained for the cyclic energy dissipation due to the inset. The validity of analytical results are confirmed by a good comparison with available test data in the literature. Expressions are then developed for the effect of the inset on fundamental natural frequency and damping ratio of the beam. The former is achieved by modifying the boundary conditions of a cantilevered beam, so as to allow for support rotation and displacement due to elasticity of the inset. The results of a series of experiments, concerning the fundamental natural frequency and damping ratio of two steel beams with a soft polymeric inset, are reported. Again, good agreement is observed between theory and experiments. The existence of an optimum inset length, resulting in maximum energy dissipation, was revealed by both theory and experiments. A further increase in the inset length beyond this value causes a reduction in energy dissipation. The effectiveness of viscoelastic boundary damping is a function of inset geometry and material properties, as well as the beam parameters, namely, its thickness, slenderness ratio and Young\u27s modulus. Results of a parametric study indicated that the increase in fundamental damping ratio due to the inset can be substantial, i.e. an order of magnitude of more for typical low damping beams. Support stiffness was found to be a strong function of the inset length. At very small inset lengths, the decrease in fundamental natural frequency can be significant. It is shown that the elastic and damping effects of the inset can be well represented by a set of discrete springs and dashpots at the support, the constants of which depend upon the geometry and material properties of the inset. The discretized inset is subsequently introduced in the formulation of numerical algorithms to determine the response of beams with a viscoelastic boundary inset to different dynamic excitations. Several illustrative problems are then presented to establish the effectiveness of viscoelastic boundary damping in a dynamic environment