Vibration of an exponentially tapered rod embedded in an elastic solid - A piecewise uniform approach

Kalkowski, Michał K., Muggleton, Jen M. and Rustghi, Emiliano (2017) Vibration of an exponentially tapered rod embedded in an elastic solid - A piecewise uniform approach. 24th International Congress on Sound and Vibration, ICSV 2017, , London, United Kingdom. 23 - 27 Jul 2017.

Abstract

Exponentially tapered rods can serve as a simplified physical model for tree roots. Based on an analytical solution for axial waves in a uniform embedded rod, we present a piecewise uniform formulation for modelling the dynamics of a tapered embedded rod. First, we revisit the uniform rod solution and discuss its characteristics. The piecewise uniform approach, in which the tapered rod is approximated as a multi-step structure composed of a number of uniform components, is presented next. The dynamics of the built-up waveguide are written in terms of propagating waves that scatter at the junctions. The assumption is made that the surrounding elastic medium has no effect on the scattering. We conduct a numerical convergence study and verify the accuracy of our model against an axisymmetric finite element (FE) simulation with perfectly absorbing boundaries. Both predictions are in very good agreement except for the low frequency range, where an assumption regarding the boundary contidions is expected to play a role. Finally, some basic observations are given in the context of the dynamics of a free tapered rod.

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