Impact Response of a Ring on Viscoelastic Foundation

This paper studies the transient responses of an elastic ring on a viscoelastic foundation (RoVEF) to suddenly applied loading. The RoVEF is a mechanical model established for analysing the dynamic behaviour of a flexible crashworthy structure (FCS) applied to bridge piers against ship-impact. Details of the RoVEF model is given, from which the free vibration modes of the structure are formulated. Two key parameters dominating the dynamic behavior of RoVEF, namely the ratio of the foundation stiffness to the ring's flexural rigidity lambda and the foundation viscous coefficient eta, are identified. The dynamic responses of RoVEF to external impact loadings are solved by using the modal superposition method. It is shown that as lambda increases, the ring is flexible and its deformation is more localized. The eta parameter facilitates the decaying of the ring's deformation to its equilibrium value. For an FCS with a relatively strong outer ring (lambda < 0.5), its impact responses can be approximated as a single degree-of-freedom mass-spring-damper system, in which the equivalent mass, spring stiffness and viscous coefficient are given in explicit forms.